CPM Homework Help : APCALC Problem 11-89

Multiple Choice: The base of a solid is the region between the curve $y = x \sin\left(x\right)$ and the $x$ -axis on the interval $0 ≤ x ≤ π$ . The cross-sections perpendicular to the $x$ -axis are semicircles. The volume of the solid is:

$1.127$

$1.271$

$1.721$

$2.171$

$2.711$

Hint:

The diameter of each semicircle is $y/2$ .
The area of each semicircle is $π\left(r^{2}\right)/2$ .
The width of each cross-section is $dx$ .

Step:

$\int_0^\pi \frac{\pi (y/2)^2}{2}dx$