Consider the following integrals involving trigonometric functions with linear arguments.

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the following integrals involving trigonometric functions with linear arguments. (a) Evaluate

I_{1}=\displaystyle\int x\,\sin 2x\,dx

. (b) Using an approach similar to part (i) or otherwise, evaluate

I_{2}=\displaystyle\int x\,\cos 2x\,dx

. Verify your answer by differentiating the result.