Question

The value of the integral ${\int }_0^2|x^2-1|dx$ is

• A. $0$
• B. $2$
• C. $-\frac{1}{3}$
• D. $-2$

Answer 1

The correct option is B $2$

${\int }_0^2|x^2-1|dx$

$={\int }_0^1-|x^2-1|dx+{\int }_1^2|x^2-1|dx$

$={[-\frac{x^3}{3}+x]}_0^1+{[\frac{x^3}{3}-x]}_1^2$

$=-\frac{1}{3}+1+\frac{8}{3}-2-\frac{1}{3}+1$

$=2$