Let be the positive number in satisfying

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

Let

c

be the positive number in

(0,1)

satisfying

\cos c = c^{2}

. Write, but do not evaluate, a definite integral expression for the volume of the solid formed when the region bounded above by

y = \cos x

and below by

y = x^{2}

0 \le x \le c

is revolved about the

x

-axis.