$\int_{-1}^{1}\left[\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right] d x=$

Question

Aicharya · Accepted Answer

Given I $=\int_{-1}^{1}\left(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}ight) d x$ Let $f(x)=\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}$ $	herefore f(-x)=\sqrt{1-x+x^{2}}-\sqrt{1+x+x^{2}}=-\left(\sqrt{1+x+x^{2}}-\sqrt{1-x-x^{2}}ight)=-f(x)$ $	herefore I=0$

$\int_{-1}^{1}\left[\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right] d x=$

Solution