What is the integral from 0 to 5 of |x^2+2x-15| ?

The integral from 0 to 5 of |x^2+2x-15| is 137/3

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integral from 0 to 5 of |x^2+2x-15|

\int_{0}^{5} x^{2} + 2 x - 15 d x

\frac{137}{3}

Decimal

45.66666 \dots

Solution steps

\int_{0}^{5} x^{2} + 2 x - 15 d x

Eliminate Absolutes

= \int_{0}^{3} - x^{2} - 2 x + 15 d x + \int_{3}^{5} x^{2} + 2 x - 15 d x

\int_{0}^{3} - x^{2} - 2 x + 15 d x = 27

\int_{3}^{5} x^{2} + 2 x - 15 d x = \frac{56}{3}

= 27 + \frac{56}{3}

Simplify

27 + \frac{56}{3} : \frac{137}{3}

= \frac{137}{3}

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What is the integral from 0 to 5 of |x^2+2x-15| ?
The integral from 0 to 5 of |x^2+2x-15| is 137/3