What is the integral from 1 to 8 of |x^2-4x-12| ?

The integral from 1 to 8 of |x^2-4x-12| is 77

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integral from 1 to 8 of |x^2-4x-12|

\int_{1}^{8} x^{2} - 4 x - 12 d x

77

Solution steps

\int_{1}^{8} x^{2} - 4 x - 12 d x

Eliminate Absolutes

= \int_{1}^{6} - x^{2} + 4 x + 12 d x + \int_{6}^{8} x^{2} - 4 x - 12 d x

\int_{1}^{6} - x^{2} + 4 x + 12 d x = \frac{175}{3}

\int_{6}^{8} x^{2} - 4 x - 12 d x = \frac{56}{3}

= \frac{175}{3} + \frac{56}{3}

Simplify

\frac{175}{3} + \frac{56}{3} : 77

= 77

What is the integral from 1 to 8 of |x^2-4x-12| ?
The integral from 1 to 8 of |x^2-4x-12| is 77