Consider the region in the first quadrant enclosed by the curves and on the closed…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region in the first quadrant enclosed by the curves y=sinx and y=cosx on the closed interval 0≤x≤2π. This region is revolved about the x-axis to form a solid.
(a) Solve sinx=cosx on the interval 0≤x≤2π, and label this point of intersection.
(b) For each sub-interval determined in part (a), indicate which curve lies farther from the x-axis.
(c) Construct the definite integral(s) representing the volume of the solid. Be sure to use the correct limits of integration for each sub-interval.
(d) Evaluate the integral expression(s) to obtain the exact volume of the solid.