CPM Homework Help : CALC Problem 8-110

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 $y = x^2$ on the interval $0 ≤ x ≤ 3$ . Help him set up this integral.

Step 1:

These cross sections are squares. Their area formula is well known.

Step 2:

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