Mathematics

Evaluate the integral $$\displaystyle\int_{-4}^{4}|x+2|\ dx$$.


SOLUTION
$$\displaystyle\int_{-4}^{4}|x+2|\ dx=\displaystyle\int_{-4}^{-2}-(x+2)\ dx+\int_{-2}^{4}(x+2) dx=\left[\dfrac{-x^{2}}{2}-2x\right]_{-4}^{-2}+\left[\dfrac{x^{2}}{2}+2x\right]_{-2}^{4}$$

$$=\dfrac {-4}{2}+4-\dfrac {16}2-8+\dfrac {16}2+8-\dfrac 42+4=-2+4-16+16-2+4=4$$

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Subjective Medium Published on 17th 09, 2020
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