Mathematics

Evaluate the integral $$\displaystyle\int_{-3}^{3}|x+1|\ dx$$.


SOLUTION
$$I=\displaystyle\int_{-3}^{3}|x+1|\ dx$$

$$I=\displaystyle\int_{-3}^{-1}|x+1|\ dx+\displaystyle\int_{-1}^{3}(x+1)\ dx$$

$$=\left[\dfrac{(x+1)^{2}}{2}\right]_{-3}^{-1}+\left[\dfrac{(x+1)^{2}}{2}\right]_{-1}^{3}$$

$$=0-\dfrac 42 +\dfrac {16}2-0 $$

$$=6$$
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Subjective Medium Published on 17th 09, 2020
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