Let the area of the region bounded by the curves y = x+a, a-x and y = x^2 be 44 3 , where a > 0 . Then the value of a is equal to

Step-by-step solution

The given curve can be rewritten as y = a+x, a-x = a - |x| . This represents an inverted V-shape with its peak at (0, a) . We need to find the points of intersection of y = a - |x| and y = x^2 . For x > 0 , the intersection occurs when a - x = x^2 x^2 + x - a = 0 . Let the positive root of this equation be r . Then, r^2 + r - a = 0 a = r^2 + r . By symmetry about the y-axis, the total area A bounded by the curves is twice the area in the first quadrant: A = 2 ₀^r (a - x - x^2) , dx = 44 3 Substitute a = r^2 + r int