Answer the following questions related to the integral involving a trigonometric function.

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

Problem

Answer the following questions related to the integral involving a trigonometric function. (i) Evaluate the indefinite integral

\displaystyle \int x\,\cos\bigl(x^{2}\bigr)\,dx

. (ii) Hence determine

\displaystyle \int_{0}^{\sqrt{\pi}} x\,\cos\bigl(x^{2}\bigr)\,dx