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Chapter 5: Q 14. (page 451)

Describe strategy for solving the type of integral given.

鈭�sinmxcosnx, one of m,n odd

Short Answer

Expert verified

If mis odd, writesinmx=sinxsinm-1x

Ifnis odd, writecosnx=cosxcosn-1x

Step by step solution

01

Step 1. Given information

Integral is鈭�sinmxcosnxdx

02

Step 2. Explanation

Consider the integral 鈭�sinmxcosnxdx

If mis odd:

localid="1648898884043" sinmx=sinxsinm-1x

Write localid="1648898918126" sin2x=1-cos2x

Then let localid="1648898927779" cosx=u

If nis odd:

cosnx=cosxcosn-1x

Write width="119">cos2x=1-sin2x

Then letsinx=v

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