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.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq