Question

The value of the integral ${\int }_{-2}^2\left(1-x^2\right|\mathrm{dx}$ is

Answer 1

${\int }_{-2}^2\left(1-x^2\right|\mathrm{dx}=2{\int }_0^2\left(1-x^2\right|\mathrm{dx}\left(\mathrm{As}\left(1-x^2\right|\mathrm{is}\mathrm{even}\mathrm{function}\right)=2\left({\int }_0^1\left(1-x^2\right)\mathrm{dx}+{\int }_1^2\left(x^2-1\right)\mathrm{dx}\right]=2\left({\left(x-\frac{x^3}{3}\right)}_0^1+{\left(\frac{x^3}{3}-x\right)}_1^2\right]=2\left(1-\frac{1}{3}+\frac{8}{3}-2-\frac{1}{3}+1\right]=4$