Question

Evaluate the integral
${\int }_{-2}^3|1-x^2|dx$

• A. $\frac{28}{3}$
• B. $\frac{14}{3}$
• C. $\frac{7}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{28}{3}$

${\int }_{-2}^3|1-x^2|dx$

${\int }_{-2}^{-1}-(1-x^2)dx+{\int }_{-1}^1(1-x^2)dx+{\int }_1^3-(1-x^2)dx$

${\int }_{-2}^{-1}-(-1+x^2)dx+{\int }_{-1}^1(1-x^2)dx+{\int }_1^3-(-1+x^2)dx$

$=-x{|}_{-2}^{-1}+\frac{x^3}{3}{|}_{-2}^{-1}+x{|}_{-1}^1\frac{-x^3}{3}{|}_{-1}^1-{|}_1^3+\frac{x^3}{3}{|}_1^3$

$=\frac{28}{3}$