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Calculus II                                                    Quiz #1                            February 14, 2005

Name____________________              R.  Hammack                               Score ______
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(1)     Find the following antiderivatives.

(a)  ∫(2x^4+x^(-1)+x+1)dx = 2/5x^5+ln|x|+x^2/2+x+C


(b)  ∫( 7^x -sec^2(x))dx = 7^x/ln(7) -tan(x)+C


(c) ∫sec(4x)tan(4x) dx = 1/4∫sec(4x)tan(4x) 4dx = 1/4∫sec(u)tan(u) 4du= 1/4sec(u)+C=1/4sec(4x)+C

u = 4x
du = 4dx


(d)   ∫cos(x)/(5 + sin(x))dx=  ∫1/(5 + sin(x))cos(x)dx=∫1/udu=ln|u|+C=ln|5+sin(x)|+C

u = 5+sin(x)
du = cos(x)dx


(2)    Find the exact value of the following sums.

(a)  Underoverscript[∑ , k = 1, arg3](2+(-1)^k/3)=  (Underoverscript[∑ , k = 1, arg3]2)+(Underoverscript[∑ , k = 1, arg3](-1)^k/3)= (100·2)+(-1/3+1/3-1/3+1/3-1/3+ ...-1/3+1/3 )
= 200 + 0 = 200


(b)  Underoverscript[∑ , k = 1, arg3]cos(2k π)= cos(2 π)+cos(4 π)+cos(6 π)+...+cos(200 π)=1+1+1+...+1 = 100