The curves and enclose a finite region in the first quadrant of the -plane.
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The curves y=x2 and y=4x−x2 enclose a finite region in the first quadrant of the xy-plane.
(i) Find the coordinates of all points where the two curves intersect.
(ii) On the same set of axes, sketch both curves and clearly shade the region that is enclosed.
(iii) Using your sketch, identify which curve serves as the upper boundary and which as the lower boundary on each sub-interval determined by the intersection abscissae. Give reasons for your answer.
(iv) Write, but do not evaluate, the definite integral or integrals that together represent the exact area of the shaded region.