M138Assign1W06wMaple

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 138 Assignment 1 Winter 2006 Submit all problems marked * on Friday, January 13, plus the questions from the Maple Addendum. 1. Evaluate the following antiderivatives and definite integrals, using a suitable change of variable, indentity, or integration by parts. π /3 1 a) 4 x ln x dx ln(x + 1) dx b) *c) 2 x sin x dx √ *e) sec θ dθ (1 − tan2 θ) dθ d) 0 0 3 f) ln 3 arctan x dx g) arcsin(2x) dx x2 e−x dx *h) −1 9 *i) 4 1 1 √ dx x−1 √ 3 *m) arctan 1 0 j) −1 1 dx x *n) √ t2 t2 − 2 cos √ *k) x dx *o) ln x dx x2 2 x3 ex dx 1 l) x arctan x dx 0 π /3 p) 0 2. Find the partial fractions decomposition of each function, and hence find a) f (x) = d) f (x) = x3 10x + 2 − 5x2 + x − 5 *b) f (x) = c) f (x) = *e) f (x) = x2 x2 + 25 x+1 x3 + x x−2 x2 − x4 *f) f (x) = x2 x4 + 3x3 + 2x2 + 1 x2 + 3x + 2 d ax (e (A sin bx + B cos bx)) = eax sin bx for all x, dx where a and b are given constants. eax sin bx dx. π e−x sin x dx. *c) Evaluate 0 t es sin(t − s) ds d) Evaluate 0 e) Verify your result in b) by...
View Full Document

This note was uploaded on 05/23/2010 for the course MATH 138 taught by Professor Anoymous during the Fall '07 term at Waterloo.

Ask a homework question - tutors are online