The area (in square units) of the region bounded by the curves y + 2 x 2 = 0 and y + 3 x 2 = 1 , is equal to

Step-by-step solution

To find point of intersection of two given curves Put y = - 2 x 2 in y + 3 x 2 = 1 ⇒   x 2 = 1 ⇒   x = ± 1 Let the given equations be y 1 = 1 - 3 x 2 and y 2 = - 2 x 2 . The desired area would be, ∫ - 1 1 y 1 - y 2 d x   = ∫ - 1 1 1 - 3 x 2 - - 2 x 2 d x = ∫ - 1 1 1 - x 2 d x = x -   x 3 3 - 1 1 =   1 - 1 3 -   - 1 + 1 3 = 2 3 -   - 2 3 = 4 3   sq .   units .