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q1solns - Mathematics 104 Quiz 1 Friday sin(2/x dx x2-2 dx...

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Unformatted text preview: Mathematics 104 Quiz 1, Friday, Feb 15, 2008 sin(2/x) dx. x2 -2 dx x2 . 1. Find Let u = 2/x. Then du = So sin(u) du = 1 cos(2/x) + C 2 sin(2/x) 1 dx = - 2 x 2 /4 2. Find 0 x sec2 x dx. Use integration by parts with u = x and dv = sec2 x dx. Then du = dx and v = tan x. So x sec2 x dx = x tan x - Evaluating at the endpoints we get ln 2 - ln( 2) + ln(1) = - 4 4 2 3. Find xn ln x dx. (Assume n = -1.) tan x dx = x tan x - ln | sec x| + C. Use integration by parts with u = ln x and dv = xn dx. Then du = dx/x and v = xn+1 /(n + 1). So xn ln x dx = xn+1 ln x - n+1 xn xn+1 ln x xn+1 dx = - +C n+1 n+1 (n + 1)2 ...
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