10Bquiz2sol

10Bquiz2sol - Quiz 2 Solution for MATH 10B, 2010 t2 + 1....

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Unformatted text preview: Quiz 2 Solution for MATH 10B, 2010 t2 + 1. (a) Find the indefinite integral 1 t2 1 t2 dt = dt Solution. t2 + (t2 + t−2 )dt 1 2+1 1 t + t −2+1 + C 2+1 −2 + 1 1 = t 3 − t −1 + C 3 13 1 = t − +C 3 t = d (b) Calculate the derivative dx x2 0 ln(1 + t2 )dt Solution. By the fundamental theorem of calculus, part 2, d dx 2. Find x2 0 ln(1 + t2 )dt = 2x · ln(1 + x4 ) 2x dx +4 x2 Solution. Let u = x2 + 4. Then du = 2xdx. So, 2x 1 dx = du x2 + 4 u = ln |u| + C = ln( x2 + 4) + C ...
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This note was uploaded on 09/07/2011 for the course MATH 10b taught by Professor Lender during the Spring '08 term at UCSD.

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