∫_ 4^4 |x+2|dx= ∫_ 4^ 2 (x+2)dx +∫_ 2^4 (x+2)dx = | x^2/2 2x |^ 2_ 4+ | x^2/2+2x |^4_ 2=20 ...

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Improper Integrals

∫-44 |x+2|dx=

Question

$\int_{- 4}^{4} | x + 2 | d x =$

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None of these

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Solution

The correct option is C 20
$\int_{- 4}^{4} | x + 2 | d x = \int_{- 4}^{- 2} - (x + 2) d x + \int_{- 2}^{4} (x + 2) d x$
$= {∣ ∣ \frac{- x^{2}}{2} - 2 x ∣ ∣}_{- 4}^{- 2} + {∣ ∣ \frac{x^{2}}{2} + 2 x ∣ ∣}_{- 2}^{4} = 20$

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