SATHEE: Indefinite Integration 1 Question 61

Indefinite Integration 1 Question 61

62. The value of $\int_{- 2}^{2} | 1 - x^{2} | d x$ is … .

(1989, 2M)

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Solution:

$\int_{- 2}^{2} | 1 - x^{2} | d x$

$= \int_{- 2}^{- 1} (x^{2} - 1) d x + \int_{- 1}^{1} (1 - x^{2}) d x + \int_{1}^{2} (x^{2} - 1) d x$

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

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

$= 4$

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