Let the straight line and the parabola enclose a finite region
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let the straight line y=4x−x2 and the parabola y=x2 enclose a finite region. Proceed as follows:
(i) Find the coordinates of their points of intersection.
(ii) Show that, on the interval obtained in part (i), the line lies above the parabola.
(iii) Calculate the exact area of the region bounded by the two curves.