A solid is formed by taking vertical square cross sections of uniform thickness…
MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A solid is formed by taking vertical square cross sections of uniform thickness through the region in the first quadrant bounded by the x-axis, the curve y=x, and the line x=4. Each square has its base lying in the xy-plane and perpendicular to the x-axis.
(a) Express the side length s(x) of a typical square cross section in terms of x.
(b) Write, but do not evaluate, a definite integral that represents the volume of the solid.
(c) Explain why your choice of the differential element in part (b) is appropriate for this situation.