Definite Integration Question 61
Question 61
- The value of $\int_{-2}^{2}\left|1-x^{2}\right| d x$ is … .
(1989, 2M)
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Solution:
- $\int_{-2}^{2}\left|1-x^{2}\right| d x$
$=\int_{-2}^{-1}\left(x^{2}-1\right) d x+\int_{-1}^{1}\left(1-x^{2}\right) d x+\int_{1}^{2}\left(x^{2}-1\right) d x$
$=\frac{x^{3}}{3}-x_{-2}^{-1}+x-{\frac{x^{3}}{3}}{-1}^{1}+\frac{x^{3}}{3}-x{1}^{2}$
$=-\frac{1}{3}+1+\frac{8}{3}-2+1-\frac{1}{3}+1-\frac{1}{3}+\frac{8}{3}-2-\frac{1}{3}+1$
$=4$
