Giai Bai Tap Tich Phan Suy Rong p2

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tich phan suy rong dhbk le xuan dai

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<ul><li><p>GII BI TP TCH PHN SUY RNG</p><p>Bi ging in t</p><p>TS. L Xun i</p><p>Trng i hc Bch Khoa TP HCM</p><p>Khoa Khoa hc ng dng, b mn Ton ng dng</p><p>Email: ytkadai@hcmut.edu.vn</p><p>TP. HCM 2015.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 1 / 36</p></li><li><p>Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1</p><p>Tnh tch phn suy rng loi 1</p><p>Cu 1</p><p>Tnh tch phn suy rng I =</p><p>+1</p><p>dx</p><p>xx2 + x + 1</p><p>.</p><p>t t =1</p><p>x x = 1</p><p>t dx = dt</p><p>t2.</p><p>i cn</p><p>x 1 +t 1 0</p><p>.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 2 / 36</p></li><li><p>Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1</p><p>Tnh tch phn suy rng loi 1</p><p>Cu 1</p><p>Tnh tch phn suy rng I =</p><p>+1</p><p>dx</p><p>xx2 + x + 1</p><p>.</p><p>t t =1</p><p>x x = 1</p><p>t dx = dt</p><p>t2.</p><p>i cn</p><p>x 1 +t 1 0</p><p>.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 2 / 36</p></li><li><p>Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1</p><p>Khi </p><p>I =</p><p>01</p><p>dtt2</p><p>1t .</p><p>1t2+ 1t + 1</p><p>=</p><p>10</p><p>dt1 + t + t2</p><p>=</p><p>10</p><p>d(t + 12</p><p>)(t + 12</p><p>)2+ 34</p><p>=</p><p>[ln</p><p>t + 12 +t2 + t + 1]1</p><p>0</p><p>= ln</p><p>(3</p><p>2+3</p><p>) ln</p><p>(3</p><p>2</p><p>)= ln</p><p>(1 +</p><p>23</p><p>).</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 3 / 36</p></li><li><p>Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1</p><p>Tnh tch phn suy rng loi 1</p><p>Cu 2</p><p>Tnh tch phn suy rng I =</p><p>+1</p><p>arctan x</p><p>x2dx .</p><p>t</p><p> u = arctan xdv = dxx2</p><p>du =</p><p>dx</p><p>1 + x2</p><p>v = 1x</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 4 / 36</p></li><li><p>Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1</p><p>Tnh tch phn suy rng loi 1</p><p>Cu 2</p><p>Tnh tch phn suy rng I =</p><p>+1</p><p>arctan x</p><p>x2dx .</p><p>t</p><p> u = arctan xdv = dxx2</p><p>du =</p><p>dx</p><p>1 + x2</p><p>v = 1x</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 4 / 36</p></li><li><p>Tch phn suy rng loi 1 Tnh tch phn suy rng loi 1</p><p>Khi </p><p>I =</p><p>[1x. arctan x</p><p>]+1</p><p>+</p><p>+1</p><p>dx</p><p>x(1 + x2)=</p><p>=pi</p><p>4+</p><p>+1</p><p>dx</p><p>x</p><p>+1</p><p>xdx</p><p>1 + x2=pi</p><p>4+</p><p>[ln |x | 1</p><p>2ln(1 + x2)</p><p>]+1</p><p>=</p><p>=pi</p><p>4+</p><p>[ln</p><p> x1 + x2]+</p><p>1</p><p>=pi</p><p>4+ ln 1 ln 1</p><p>2=pi</p><p>4+</p><p>ln 2</p><p>2</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 5 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p> ngha hnh hc</p><p>Trong trng hp f (x) &gt; 0,x [a,+), gi trca tch phn suy rng hi t c ngha hnh hc</p><p>l din tch ca hnh phng v hn c gi hn</p><p>bi x = a, trc Ox v th hm f (x)</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 6 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Ch .</p><p>T ngha hnh hc ca tch phn suy rng, ta</p><p>c nu tn ti gii hn hu hn v khc 0</p><p>limx+ f (x) = A 6= 0</p><p>v f (x) kh tch trn mi on [a, b] [a,+)th tch phn suy rng</p><p>+a</p><p>f (x)dx phn k</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 7 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>1</p><p>Nu &gt; 1 th I =+a</p><p>dx</p><p>xhi t.</p><p>2</p><p>Nu 6 1 th I =+a</p><p>dx</p><p>xphn k.</p><p>1</p><p>Nu &gt; 1 th I =+2</p><p>dx</p><p>x. ln xhi t.</p><p>2</p><p>Nu &lt; 1 th I =+2</p><p>dx</p><p>x. ln xphn k.</p><p>3</p><p>Nu = 1 th I =+2</p><p>dx</p><p>x. ln xhi t nu</p><p> &gt; 1, phn k nu 6 1.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>1</p><p>Nu &gt; 1 th I =+a</p><p>dx</p><p>xhi t.</p><p>2</p><p>Nu 6 1 th I =+a</p><p>dx</p><p>xphn k.</p><p>1</p><p>Nu &gt; 1 th I =+2</p><p>dx</p><p>x. ln xhi t.</p><p>2</p><p>Nu &lt; 1 th I =+2</p><p>dx</p><p>x. ln xphn k.</p><p>3</p><p>Nu = 1 th I =+2</p><p>dx</p><p>x. ln xhi t nu</p><p> &gt; 1, phn k nu 6 1.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>1</p><p>Nu &gt; 1 th I =+a</p><p>dx</p><p>xhi t.</p><p>2</p><p>Nu 6 1 th I =+a</p><p>dx</p><p>xphn k.</p><p>1</p><p>Nu &gt; 1 th I =+2</p><p>dx</p><p>x. ln xhi t.</p><p>2</p><p>Nu &lt; 1 th I =+2</p><p>dx</p><p>x. ln xphn k.</p><p>3</p><p>Nu = 1 th I =+2</p><p>dx</p><p>x. ln xhi t nu</p><p> &gt; 1, phn k nu 6 1.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>1</p><p>Nu &gt; 1 th I =+a</p><p>dx</p><p>xhi t.</p><p>2</p><p>Nu 6 1 th I =+a</p><p>dx</p><p>xphn k.</p><p>1</p><p>Nu &gt; 1 th I =+2</p><p>dx</p><p>x. ln xhi t.</p><p>2</p><p>Nu &lt; 1 th I =+2</p><p>dx</p><p>x. ln xphn k.</p><p>3</p><p>Nu = 1 th I =+2</p><p>dx</p><p>x. ln xhi t nu</p><p> &gt; 1, phn k nu 6 1.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>1</p><p>Nu &gt; 1 th I =+a</p><p>dx</p><p>xhi t.</p><p>2</p><p>Nu 6 1 th I =+a</p><p>dx</p><p>xphn k.</p><p>1</p><p>Nu &gt; 1 th I =+2</p><p>dx</p><p>x. ln xhi t.</p><p>2</p><p>Nu &lt; 1 th I =+2</p><p>dx</p><p>x. ln xphn k.</p><p>3</p><p>Nu = 1 th I =+2</p><p>dx</p><p>x. ln xhi t nu</p><p> &gt; 1, phn k nu 6 1.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 8 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 3</p><p>Tm tch phn sau hi t I =</p><p>+1</p><p>dx</p><p>x 31 + x2</p><p>1</p><p>x 31 + x2</p><p>x+ 1x.x2/3</p><p>=1</p><p>x+2/3</p><p> tch phn I hi t th +2</p><p>3&gt; 1 &gt; 1</p><p>3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 9 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 3</p><p>Tm tch phn sau hi t I =</p><p>+1</p><p>dx</p><p>x 31 + x2</p><p>1</p><p>x 31 + x2</p><p>x+ 1x.x2/3</p><p>=1</p><p>x+2/3</p><p> tch phn I hi t th +2</p><p>3&gt; 1 &gt; 1</p><p>3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 9 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 4</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+1</p><p>(2x + 3)dx</p><p>(4 + x) 31 + x4</p><p>Trng hp 1: &gt; 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2xx.x4/3</p><p>=2</p><p>x+1/3</p><p> tch phn I hi t th +1</p><p>3&gt; 1 &gt; 2</p><p>3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 10 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 4</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+1</p><p>(2x + 3)dx</p><p>(4 + x) 31 + x4</p><p>Trng hp 1: &gt; 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2xx.x4/3</p><p>=2</p><p>x+1/3</p><p> tch phn I hi t th +1</p><p>3&gt; 1 &gt; 2</p><p>3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 10 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2x5.x4/3</p><p>=2</p><p>5x1/3</p><p>I phn k v1</p><p>3&lt; 1</p><p>Trng hp 3: &lt; 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2x4.x4/3</p><p>=1</p><p>2x1/3</p><p>I phn k v1</p><p>3&lt; 1.</p><p>Vy tch phn I hi t th &gt; 2/3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 11 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2x5.x4/3</p><p>=2</p><p>5x1/3</p><p>I phn k v1</p><p>3&lt; 1</p><p>Trng hp 3: &lt; 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2x4.x4/3</p><p>=1</p><p>2x1/3</p><p>I phn k v1</p><p>3&lt; 1.</p><p>Vy tch phn I hi t th &gt; 2/3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 11 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2x5.x4/3</p><p>=2</p><p>5x1/3</p><p>I phn k v1</p><p>3&lt; 1</p><p>Trng hp 3: &lt; 0</p><p>(2x + 3)</p><p>(4 + x) 31 + x4</p><p>x+ 2x4.x4/3</p><p>=1</p><p>2x1/3</p><p>I phn k v1</p><p>3&lt; 1.</p><p>Vy tch phn I hi t th &gt; 2/3.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 11 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 5</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+1</p><p>(3x + 4x)dx(5 + x)1</p><p>Trng hp 1: &gt; 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4xx(1)</p><p>=4</p><p>x(1)1</p><p> tch phn I hi t th</p><p>( 1) 1 &gt; 1 &gt; 2 &lt; 1 &gt; 2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 12 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 5</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+1</p><p>(3x + 4x)dx(5 + x)1</p><p>Trng hp 1: &gt; 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4xx(1)</p><p>=4</p><p>x(1)1</p><p> tch phn I hi t th</p><p>( 1) 1 &gt; 1 &gt; 2 &lt; 1 &gt; 2.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 12 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4x61</p><p>=4</p><p>61.x1</p><p>I phn k v 1 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4x51</p><p>=4</p><p>51.x1</p><p>I phn k v 1 &lt; 1Vy tch phn I hi t th &gt; 2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 13 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4x61</p><p>=4</p><p>61.x1</p><p>I phn k v 1 &lt; 1Trng hp 3: &lt; 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4x51</p><p>=4</p><p>51.x1</p><p>I phn k v 1 &lt; 1</p><p>Vy tch phn I hi t th &gt; 2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 13 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4x61</p><p>=4</p><p>61.x1</p><p>I phn k v 1 &lt; 1Trng hp 3: &lt; 0</p><p>(3x + 4x)(5 + x)1</p><p>x+ 4x51</p><p>=4</p><p>51.x1</p><p>I phn k v 1 &lt; 1Vy tch phn I hi t th &gt; 2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 13 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 6</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+3</p><p>ex + ln x(1 + x)2</p><p>dx</p><p>Trng hp 1: &gt; 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln xx(2)</p><p>=1</p><p>x(2). ln1 x</p><p> tch phn I hi t th ( 2) &gt; 1 &gt; 1 +2 &lt; 12 &gt; 1 +2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 14 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 6</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+3</p><p>ex + ln x(1 + x)2</p><p>dx</p><p>Trng hp 1: &gt; 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln xx(2)</p><p>=1</p><p>x(2). ln1 x</p><p> tch phn I hi t th ( 2) &gt; 1 &gt; 1 +2 &lt; 12 &gt; 1 +2.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 14 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln x22</p><p>=1</p><p>22.x0 ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln x1</p><p>=1</p><p>x0 ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Vy tch phn I hi t th &gt; 1 +2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 15 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln x22</p><p>=1</p><p>22.x0 ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln x1</p><p>=1</p><p>x0 ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Vy tch phn I hi t th &gt; 1 +2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 15 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln x22</p><p>=1</p><p>22.x0 ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>ex + ln x(1 + x)2</p><p>x+ ln x1</p><p>=1</p><p>x0 ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Vy tch phn I hi t th &gt; 1 +2.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 15 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 7</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+2</p><p>exdx</p><p>(x 1) ln x</p><p>Trng hp 1: &gt; 0</p><p>ex</p><p>(x 1) ln xx+ e</p><p>x</p><p>x ln xx+ +</p><p>Do , tch phn I phn k.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 16 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Cu 7</p><p>Tm tch phn sau hi t</p><p>I =</p><p>+2</p><p>exdx</p><p>(x 1) ln x</p><p>Trng hp 1: &gt; 0</p><p>ex</p><p>(x 1) ln xx+ e</p><p>x</p><p>x ln xx+ +</p><p>Do , tch phn I phn k.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 16 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>ex</p><p>(x 1) ln xx+ 1</p><p>ln x=</p><p>1</p><p>x0. ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>ex</p><p>(x 1) ln x =(x 1)ex</p><p>ln xx+ x</p><p>ex</p><p>ln x</p><p>xexln x1x2</p><p>=x+2</p><p>ex . ln xx+ 0</p><p>Vy tch phn I hi t th &lt; 0.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 17 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>ex</p><p>(x 1) ln xx+ 1</p><p>ln x=</p><p>1</p><p>x0. ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>ex</p><p>(x 1) ln x =(x 1)ex</p><p>ln xx+ x</p><p>ex</p><p>ln x</p><p>xexln x1x2</p><p>=x+2</p><p>ex . ln xx+ 0</p><p>Vy tch phn I hi t th &lt; 0.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 17 / 36</p></li><li><p>Tch phn suy rng loi 1 Tm tch phn suy rng loi 1 hi t</p><p>Trng hp 2: = 0</p><p>ex</p><p>(x 1) ln xx+ 1</p><p>ln x=</p><p>1</p><p>x0. ln1 x</p><p>I phn k v 0 &lt; 1</p><p>Trng hp 3: &lt; 0</p><p>ex</p><p>(x 1) ln x =(x 1)ex</p><p>ln xx+ x</p><p>ex</p><p>ln x</p><p>xexln x1x2</p><p>=x+2</p><p>ex . ln xx+ 0</p><p>Vy tch phn I hi t th &lt; 0.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 17 / 36</p></li><li><p>Tch phn suy rng loi 2 Tnh tch phn suy rng loi 2</p><p> ngha hnh hc</p><p>Trong trng hp f (x) &gt; 0,x [a, b), gi trca tch phn suy rng hi t c ngha hnh hc</p><p>l din tch ca hnh phng v hn c gi hn</p><p>bi x = a, x = b trc Ox v th hm f (x),</p><p>trong x = b l tim cn ng ca hm s f (x)</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 18 / 36</p></li><li><p>Tch phn suy rng loi 2 Tnh tch phn suy rng loi 2</p><p> ngha hnh hc</p><p>Trong trng hp f (x) &gt; 0,x (a, b], gi trca tch phn suy rng hi t c ngha hnh hc</p><p>l din tch ca hnh phng v hn c gi hn</p><p>bi x = a, x = b trc Ox v th hm f (x),</p><p>trong x = a l tim cn ng ca hm s f (x)</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 19 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>Nu hm s f (x) khng b chn khi x c, vic (a, b) th tch phn suy rng b</p><p>a</p><p>f (x)dx =</p><p> ca</p><p>f (x)dx +</p><p> bc</p><p>f (x)dx</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 20 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>nh l</p><p>Tch phn suy rng</p><p>ba</p><p>f (x)dx c gi l hi t</p><p>nu c 2 tch phn</p><p>ca</p><p>f (x)dx v</p><p>bc</p><p>f (x)dx u hi</p><p>t khng ph thuc ln nhau.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 21 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>1</p><p>Nu &lt; 1 th tch phnba</p><p>dx</p><p>(b x) vba</p><p>dx</p><p>(x a) hi t</p><p>2</p><p>Nu &gt; 1 th tch phnba</p><p>dx</p><p>(b x) vba</p><p>dx</p><p>(x a) phn k</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 22 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>Cu 8</p><p>Tnh tch phn suy rng loi 2</p><p>I =</p><p>31</p><p>dx4x x2 3</p><p>I =</p><p>31</p><p>d(x 2)1 (x 2)2 = arcsin(x 2)</p><p>31=</p><p>= arcsin 1 arcsin(1) = pi2+pi</p><p>2= pi.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 23 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>Cu 8</p><p>Tnh tch phn suy rng loi 2</p><p>I =</p><p>31</p><p>dx4x x2 3</p><p>I =</p><p>31</p><p>d(x 2)1 (x 2)2 = arcsin(x 2)</p><p>31=</p><p>= arcsin 1 arcsin(1) = pi2+pi</p><p>2= pi.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 23 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>Cu 9</p><p>Tnh tch phn suy rng loi 2</p><p>I =</p><p>20</p><p>dx</p><p>(x 1)x2 x + 1</p><p>I =</p><p>10</p><p>dx</p><p>(x 1)x2 x + 1+2</p><p>1</p><p>dx</p><p>(x 1)x2 x + 1 = I1+I2</p><p>Tch phn I hi t khi c hai tch phn I1, I2 cng hi t.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 24 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>Cu 9</p><p>Tnh tch phn suy rng loi 2</p><p>I =</p><p>20</p><p>dx</p><p>(x 1)x2 x + 1</p><p>I =</p><p>10</p><p>dx</p><p>(x 1)x2 x + 1+2</p><p>1</p><p>dx</p><p>(x 1)x2 x + 1 = I1+I2</p><p>Tch phn I hi t khi c hai tch phn I1, I2 cng hi t.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 24 / 36</p></li><li><p>Tch phn suy rng loi 2 nh ngha tch phn</p><p> ba f (x)dx, c [a, b] l im gin on</p><p>1</p><p>(x 1)x2 x + 1x1 1</p><p>(x 1)12 1 + 1</p><p>=1</p><p>(x 1)1Tch phn I1 phn k. Vy I cng phn k.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 25 / 36</p></li><li><p>Tch phn suy rng loi 2 Tm tch phn suy rng loi 2 hi t</p><p>Cu 10</p><p>Tm tch phn sau hi t I =</p><p>pi0</p><p>1 cos xx</p><p>dx .</p><p>1 cos xx</p><p>x0+x2</p><p>2</p><p>x=</p><p>1</p><p>2x2</p><p> tch phn I hi t th 2 &lt; 1 &lt; 3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 26 / 36</p></li><li><p>Tch phn suy rng loi 2 Tm tch phn suy rng loi 2 hi t</p><p>Cu 10</p><p>Tm tch phn sau hi t I =</p><p>pi0</p><p>1 cos xx</p><p>dx .</p><p>1 cos xx</p><p>x0+x2</p><p>2</p><p>x=</p><p>1</p><p>2x2</p><p> tch phn I hi t th 2 &lt; 1 &lt; 3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 26 / 36</p></li><li><p>Tch phn suy rng loi 2 Tm tch phn suy rng loi 2 hi t</p><p>Cu 11</p><p>Tm tch phn sau hi t</p><p>I =</p><p>10</p><p>e2 + x2 ecos x</p><p>xdx .</p><p>e2 + x2 ecos x</p><p>xx0+</p><p>e[(</p><p>1 + 12 .x2</p><p>e2</p><p>)(1 x22</p><p>)]x</p><p>=1 + e2</p><p>2e.</p><p>1</p><p>x2</p><p> tch phn I hi t th 2 &lt; 1 &lt; 3.</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 27 / 36</p></li><li><p>Tch phn suy rng loi 2 Tm tch phn suy rng loi 2 hi t</p><p>Cu 11</p><p>Tm tch phn sau hi t</p><p>I =</p><p>10</p><p>e2 + x2 ecos x</p><p>xdx .</p><p>e2 + x2 ecos x</p><p>xx0+</p><p>e[(</p><p>1 + 12 .x2</p><p>e2</p><p>)(1 x22</p><p>)]x</p><p>=1 + e2</p><p>2e.</p><p>1</p><p>x2</p><p> tch phn I hi t th 2 &lt; 1 &lt; 3.TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 27 / 36</p></li><li><p>Tch phn suy rng loi 2 Tm tch phn suy rng loi 2 hi t</p><p>Cu 12</p><p>Tm tch phn sau hi t</p><p>I =</p><p>20</p><p>xdx3</p><p>(x 1)(x 2)2 .</p><p>TS. L Xun i (BK TPHCM) GII BI TP TCH PHN SUY RNG TP. HCM 2015. 28 / 36</p></li><li><p>Tch phn suy rng loi 2 Tm tch phn suy rng loi 2 hi t</p><p>Trng hp 1: &gt; 0</p><p>I =</p><p>10</p><p>xdx3</p><p>(x 1)(x 2)2+3/21</p><p>xdx3</p><p>(x