A solid has a base in the xy-plane that is the region enclosed by the curves and
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A solid has a base in the xy-plane that is the region enclosed by the curves x=y2 and x=4. Cross sections of the solid taken perpendicular to the y-axis are squares.
(a) For a fixed value of y with −2≤y≤2, describe in words the location and length of the side of the square cross section.
(b) Write, but do not evaluate, a definite integral whose value equals the volume of the solid.
(c) Explain in complete sentences why the integrand you wrote in part (b) correctly represents the area of the square cross section at height y. Be sure to reference both bounding curves in your explanation.