What is the integral from 1 to 7 of |x^2-2x-15| ?

The integral from 1 to 7 of |x^2-2x-15| is 184/3

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integral from 1 to 7 of |x^2-2x-15|

\int_{1}^{7} x^{2} - 2 x - 15 d x

\frac{184}{3}

Decimal

61.33333 \dots

Solution steps

\int_{1}^{7} x^{2} - 2 x - 15 d x

Eliminate Absolutes

= \int_{1}^{5} - x^{2} + 2 x + 15 d x + \int_{5}^{7} x^{2} - 2 x - 15 d x

\int_{1}^{5} - x^{2} + 2 x + 15 d x = \frac{128}{3}

\int_{5}^{7} x^{2} - 2 x - 15 d x = \frac{56}{3}

= \frac{128}{3} + \frac{56}{3}

Simplify

\frac{128}{3} + \frac{56}{3} : \frac{184}{3}

= \frac{184}{3}

What is the integral from 1 to 7 of |x^2-2x-15| ?
The integral from 1 to 7 of |x^2-2x-15| is 184/3