   Chapter 7.2, Problem 41E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ sin 8 x   cos 5 x   d x

To determine

To evaluate: The trigonometric integral sin8xcos5xdx

Explanation

Trigonometric integral of the form sinmxcosnxdx can be solved using the identity for sinAcosA.

Formula used:

The identity sinAcosB=12[sin(AB)+sin(A+B)].

Given:

The integral, sin8xcos5xdx.

Calculation:

Use the identity sinAcosB=12[sin(AB)+sin(A+B)] with A as 8 x and B as 5 x:

sin8xcos5xdx=12(sin(8x5x)+sin(8x+5x))dx<

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