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Calculus II                                                       Quiz #4                                April 1, 2005

Name____________________                 R.  Hammack                            Score ______
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Evaluate the following integrals.

(a)    ∫x cos(5x) dx =(x sin(5x))/5-∫sin(5x)/5 dx=(x sin(5x))/5+cos(5x)/25 +C

u = x              dv = cos(5x) dx  du = dx      v = sin(5x)/5



(b)     ∫sec(x^(1/2))/x^(1/2)dx =

2∫sec(x^(1/2)) 1/(2x^(1/2)) dx = 2∫sec(u) du = 2ln | sec(u) + tan(u) | +C  = 2ln | sec(x^(1/2)) + tan(x^(1/2)) | +C


u = x^(1/2)  du = 1/(2x^(1/2)) dx



(c)    ∫sin^5(x/3)cos(x/3)dx =3∫(sin(x/3))^5cos(x/3)1/3dx =3∫u^5du =3u^6/6+C=sin^6(x/3)/2+C

u = sin(x/3)  du = cos(x/3) 1/3dx

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