### Home > CALC > Chapter 10 > Lesson 10.1.3 > Problem10-19

10-19.

Without your calculator, find the volume generated when the region bounded by $f(x) = x\operatorname{cos} x + 3$ and the $x$-axis for $0 ≤ x ≤ π$ is rotated about the $y$-axis. Then, check your answer with your graphing calculator.

Use shells:
$\int_0^\text{?}2\pi x(f(x))dx$
You will need to use integration by parts twice.