   Chapter 7.R, Problem 2CC

Chapter
Section
Textbook Problem

# How do you evaluate ∫ sin m x cos n x   d x if m is odd? What if n is odd? What if m and n are both even?

To determine

To Find: Integral of the type sinmxcosndx

Explanation

If m is odd, then m = 2 k + 1 for some integer k. Now,

sinmxcosnxdx=sin2k+1xcosnxdx=sin2kxcosnxsinxdx=(1cos2x)kcosnxsinxdx

Substitute cosx=t, and then ultimately you will get a polynomial as an integrand which is easily integrable.

Again if n is odd, then n = 2 k + 1 for some integer k

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