MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Let C1 be the curve y=x3−4x and let C2 be the line y=x. The two curves intersect in three distinct points, enclosing one finite region.
(i) Find the coordinates of the three points of intersection of C1 and C2.
(ii) Show that the finite region bounded only by the two curves lies entirely between the leftmost and rightmost intersection points found in part (i).
(iii) Taking into account any change in which curve is above the other, set up all the definite integral(s) required to find the exact area of this bounded region.
(iv) Evaluate the integral(s) obtained in part (iii) to determine the exact area.