The base of a solid is the region in the first quadrant bounded above by the line y = 5, below by y = sin−1(x), and to the right by the line x = 1. For this solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid?

Each cross section is a square with side length equal to the vertical distance between the curves and , with , or . Then each section has an area of , so the volume of this solid is

For computing the integral, consider the substitution

Then the integral becomes

Integrate by parts twice; for the first round, take

For the second round, take

and the rest is trivial.

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.