M138.W09.assmt1

M138.W09.assmt1 - MATH 138 Assignment 1 (2 pages) Winter...

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Unformatted text preview: MATH 138 Assignment 1 (2 pages) Winter 2009 Submit all problems marked * by 8:20 a.m. on Friday, January 16. 1. Evaluate the following antiderivatives and definite integrals, using a suitable change of variable, identity, or integration by parts. *a) Z x 4 ln x dx b) Z 1 ln( x + 1) dx c) Z x 2 sin x dx *d) Z π/ 3 (1- tan 2 θ ) dθ *e) Z sec θ dθ f) Z √ 3- 1 arctan x dx *g) Z arcsin(2 x ) dx *h) Z ln 3 x 2 e- x dx i) Z 9 4 1 √ x- 1 dx j) Z 1- 1 √ t 2 t 2- 2 dt *k) Z ln x x 2 dx l) Z 1 x arctan x dx *m) Z √ 3 1 arctan ( 1 x ) dx n) Z cos √ x dx *o) Z x 3 e x 2 dx *p) Z π/ 3 1 sin x- 1 dx q) Z x √ x 2- 9 dx *r) Z 2 x 3 √ 4- x 2 dx s) Z 2 x 3 x 2 + 4 dx *t) Z x 2 ( x 2 + a 2 ) 3 / 2 dx u) Z √ x ln x dx v) Z sin ln x dx *w) Z 1 x 3 √ 4 + x 2 dx *x) Z (ln x ) 2 dx h hints : For part e), multiply sec θ by sec θ + tan θ tan θ + sec θ ; for part o), w), think x 3 = x 2 · x....
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This note was uploaded on 09/04/2009 for the course MATH 138 taught by Professor Anoymous during the Winter '07 term at Waterloo.

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M138.W09.assmt1 - MATH 138 Assignment 1 (2 pages) Winter...

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