Let be the region in the first quadrant bounded above by the line
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let R be the region in the first quadrant bounded above by the line y=x, below by the x-axis, and on the right by the vertical line x=2. A solid is constructed so that every cross section perpendicular to the y-axis is a square.
(a) Determine the y-coordinate of the highest point in R.
(b) Set up and evaluate a definite integral that gives the volume of the solid. Express your answer as an exact value.