   Chapter 7.R, Problem 26E

Chapter
Section
Textbook Problem

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

To determine

To Find:xsinxcosxdx

Explanation

Formula Used:uvdt=uvdtu'(vdt)dt

Calculation:

Rewrite the integrand to make it as the product of two functions as shown below:

xsinxcosxdx=12x×2sinxcosxdx=12x×sin2xdx

Now, the integrand is the product of tow functions with known integrals. So, the one method which comes first in mind is the integration by parts.

Let u=x and v=sin2x and then use the formula mentioned above to find the integral

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