If the area of the region (x, y) : |2y - a| a - 2x^2 is 72 (where a > 0 ), then the value of a is

Step-by-step solution

Given the region (x, y) : |2y - a| a - 2x^2 . This inequality can be rewritten as: -(a - 2x^2) 2y - a a - 2x^2 Adding a to all parts: 2x^2 2y 2a - 2x^2 Dividing by 2 : x^2 y a - x^2 The region is bounded by the upward-opening parabola y = x^2 and the downward-opening parabola y = a - x^2 . To find the points of intersection, we equate the two curves: x^2 = a - x^2 2x^2 = a x = a 2 The area of the region is given by the integral of the upper curve minus the lower curve: Area = _ - a/2 ^ a/2 ( (a - x^2) - x^2 ) dx Ar