Question

The value of ${\int }_{-2}^3|1-x^2|dx$ is

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

Answer 1

Answer: (C)

${\int }_{-2}^3|1-x^2|dx$ $={\int }_{-2}^{-1}(x^2-1)dx+{\int }_{-1}^1(1-x^2)dx$ $+{\int }_1^3(x^2-1)dx$ $={\left[\frac{x^3}{3}-x\right]}_{-2}^{-1}+{\left[x-\frac{x^3}{3}\right]}_{-1}^1+{\left[\frac{x^3}{3}-x\right]}_1^3$ $=\frac{2}{3}+\frac{2}{3}+2\left(\frac{2}{3}\right)+(9-3)-\left(\frac{1}{3}-1\right)$ $=\frac{28}{3}$