Question

${\int }_0^2|x^2+2x-3|dx=$

• A. -1
• B. 4
• C. 2
• D. 0

Answer 1

The correct option is B 4

${\int }_0^2|x^2+2x-3|dx$
${\int }_0^1-(x^2+2x-3)dx+{\int }_1^2(x^2+2x-3)dx$
$-\frac{x^3}{3}{\int }_0^1-2\left(\frac{x^2}{2}\right){\int }_0^1+3{\int }_0^1+\frac{x^3}{3}{\int }_1^2+2\left(\frac{x^2}{2}\right){\int }_1^2-3{\int }_1^2$
$2-\left(1\right)+(4-1)$
$=4$