Mathematics

Problem

The curves

y = \sin x

and

y = \cos x

intersect at

x = \dfrac{\pi}{4}

. The region bounded by these curves on

0 \le x \le \dfrac{\pi}{2}

is revolved about the line

y = \tfrac{1}{2}

. Write the definite integral(s) whose sum equals the volume of the solid. Do not evaluate.