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Q.

$\int_{- 2}^{2} |1 - x^{2}| d x$ is equal to :

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a

2

b

4

c

6

d

8

answer is B.

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Detailed Solution

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$\begin{array}{l} I = \int_{- 2}^{2} |1 - x^{2}| d x = \int_{- 2}^{- 1} |1 - x^{2}| d x + \int_{- 1}^{1} |1 - x^{2}| d x \\ + \int_{1}^{2} |1 - x^{2}| d x \\ \Rightarrow I = - \int_{- 2}^{- 1} (1 - x^{2}) d x + \int_{- 1}^{1} (1 - x^{2}) d x - \int_{1}^{2} (1 - x^{2}) d x \\ \Rightarrow I = \frac{4}{3} + \frac{4}{3} + \frac{4}{3} = 4 . \end{array}$

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∫−22 1−x2dx is equal to :