Question

Find the area of the region bounded by the curves of y=1-2x^2 and y=|x|

Answer 1

The area of interest is symmetrical about the origin, so can be found by doubling the integral for the area in the first quadrant. Then the total area is

`A= 2\int\limits^(0.5)_(0){(1-2x^2-x)} \, dx =2\left(0.5-(2)/(3)0.5^(3)-(1)/(2)0.5^2\right)\\A=1-(1)/(6)-(1)/(4)=1-(5)/(12)\\\\A=(7)/(12)`