### Home > APCALC > Chapter 8 > Lesson 8.3.2 > Problem8-111

8-111.

Uh-oh! Arlen needs your help. He is trying to write an integral for the volume of square cross-sections perpendicular to the $y$-axis where the base is the region bounded by the $y$-axis and $y = x^2$ over the interval $0 ≤ x ≤ 3$. Help him set up this integral.

$\text{volume by cross-sections }= \int_{x=a}^{x=b}(A(x))dx\text{ or }\text{volume by cross-sections }= \int_{y=a}^{y=b}(A(y))dy$

These cross-sections are squares. This area formula is well known.

The function and the bounds must be in terms of $y$, because the cross-sections are perpendicular to the $y$-axis.
Rewrite the function in terms of $y$ and determine the $y$-values that correspond with the given domain.