Two curves, the parabola and the line , enclose a finite region in the…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Two curves, the parabola x=y2−4y+3 and the line x=2y−1, enclose a finite region T in the plane.
(a) Find all y-values at which the two curves intersect.
(b) Determine the sub-intervals of the intersection interval on which each curve serves as the right-hand boundary of T. Give reasons for your conclusion.
(c) Set up (but do not yet evaluate) the definite integral or sum of integrals that represents the exact area of T.
(d) Evaluate the integral(s) from part (c) to obtain the exact area of the region.