Consider the region bounded by the graphs of and for
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region T bounded by the graphs of y=x and y=2−x for 0≤x≤2. The region is revolved about the x-axis.
(a) Find the coordinates of the point where the graphs of y=x and y=2−x intersect.
(b) Using the result from part (a), determine on which subinterval each of the two functions is farther from the x-axis and which is closer. Provide justification for your conclusion.
(c) Write the definite integral or integrals that must be evaluated to compute the exact volume of the solid generated by revolving region T about the x-axis.
(d) Evaluate the integral expression(s) from part (c) to obtain the exact volume of the solid in terms of π. Show all algebraic steps leading to your answer.