Question

I am really struggling on the Calculus 2 volumes by integration. I've managed on my own until this chapter. I really need to understand the steps, not just the answer.

Find the volume of the solid. The base is the triangle enclosed by the following.
x + y = 10, the x-axis, and the y-axis
The cross sections perpendicular to the y-axis are semicircles.

Answer 1

use V = \[\pi \int\limits_{0}^{10} y^2 dx\]

y^2 = (10 - x)^2 or 100 - 20x _ x^2

the problem becomes \[V = \pi \int\limits_{0}^{10} 10 - 20x + x^2 dx\]