Find the area of bounded region f(x) =x^4_2x^2 and g(x) =2x^2

dear student
dy/dx = 4x^3 - 6x^2 + 2x


for maxima or minima; dy/dx=0

4x^3 - 6x^2 + 2x = 0

x = 1, 1/2, 0

d^2y/dx^2 = 12x^2 - 12x + 2

at x = 0; d^2y/dx^2 = +ve

and at x = 1, 1/2; d^2y/dx^2 = -ve

therefore point of minima = 1, 1/2

Area= integration of y(x) from 1/2 ( lower limit ) to 1 ( upper limit)
hope it helps