Question

Integrate from -5 to 5 |x+2| dx​

Answer 1

Explanation:

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Answer 2

$\int ^{5} _{ - 5} |x + 2|$

$\implies \int _{-5} ^{5} \frac{ {x}^{2} }{2} + x$

$\implies [ \frac{ {x}^{2} }{2} + x] _{-5} ^{5}$

$\implies [ \frac{ {(5)}^{2} }{2} + 2(5)] - [ \frac{ {( - 5)}^{2} }{2} + 2( - 5) ]$

$\implies [ \frac{ {25}}{2} + 10] - [ \frac{ 25 }{2} - 10 ]$

$\implies \frac{ {25}}{2} + 10- \frac{ 25 }{2} + 10$

$\orange{ \therefore \int ^{5} _{ - 5} |x + 2| = 20 }$