### Home > APCALC > Chapter 10 > Lesson 10.1.3 > Problem10-29

10-29.

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

$\$

Use shells:

$\int_0^\text{?}2\pi x(f(x))dx$

You will need to use integration by parts twice.