Science:Math Exam Resources/Courses/MATH101 C/April 2025/Question 06/Statement

Consider the region $R$ in the first quadrant bounded by the $x$-axis and the curves $y=x^{-n}$ and $y=x^n$, where $n>1$ is a real number.

Region $R$ bounded by the $x$-axis and the curves $y=x^{-n}$ and $y=x^n$.

Find the volume $V(n)$ of the solid generated by revolving $R$ about the $x$-axis. Express your answer in terms of $n$.