- 4 4 | x + 2 | d x =

Question

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

Smart Achievers · Accepted Answer

(3)

Ans. 20

Explanation :

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

$= {[\frac{- x^{2}}{2} - 2 x]}_{- 4}^{- 2} + {[\frac{x^{2}}{2} + 2 x]}_{- 2}^{4}$

$= [\frac{- 4}{2} + 4 + \frac{16}{2} - 8] + [\frac{16}{2} + 8 - \frac{4}{2} + 4]$

$= 2 + 18$

$= 20$

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