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Calculus II                                                          Quiz #1                                             February 17, 2003

Name____________________                   R.  Hammack                                                 Score ______
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Find the following antiderivatives.

(a)  ∫ (3x^5 + sec^2(x) + e ) dx =3x^6/6 + tan(x) + e x + C= x^6/2 + tan(x) + e x + C



(b)  ∫7/x^2dx = 7∫x^(-2) dx =7x^(-1)/-1 + C = -7/x + C



(c) ∫ (1/x + cos(x)) dx =ln | x | +sin(x) + C



(d)   ∫x/(x^2 + 4) dx =1/2∫ (2x)/(x^2 + 4) dx =1/2∫1/udu =ln | u | +C = 1/2ln | x^2 + 4 | + C

u = x^2 + 4
du = 2x dx


(e) ∫cos^2(x)   sin(x) dx =-∫ (cos(x))^2 (- sin(x)) dx =-∫u^2d u =-u^3/3 + C= -cos^3(x)/3 + C

u = cos(x)
du = -sin(x) dx


(f) ∫cos(8x)   dx =1/8∫cos(8x)   8dx =1/8∫cos(u)   du =1/8sin(u) + C = 1/8sin(8x) + C

u = 8x
du = 8dx