The correct option is A 4 ∫ _ 2 ^ 2 | 1 x ^ 2 | dx = ∫ _ 2 ^ 1 ( 1 x ^ 2 ) #160; dx +∫ _ 1 ^ 1 ( 1 x ^ 2 ) #160; dx ∫ _ 1 ^ 2 ( 1 ...

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Integration by Substitution

∫-22 | 1-x2 |...

Question

$\int_{- 2}^{2} ∣ ∣ 1 - x^{2} ∣ ∣ d x$ is

4

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Solution

The correct option is A $4$
$\int_{- 2}^{2} ∣ ∣ 1 - x^{2} ∣ ∣ d x = - \int_{- 2}^{- 1} (1 - x^{2}) d x$

$+ \int_{- 1}^{1} (1 - x^{2}) d x - \int_{1}^{2} (1 - x^{2}) d x$
$= - {[x - \frac{x^{3}}{3}]}_{1}^{2} + {[x - \frac{x^{3}}{3}]}_{- 1}^{1} - {[x - \frac{x^{3}}{2}]}_{- 1}^{2} = 4$

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