What is the integral from 1 to 4 of |x^2-2x-15| ?

The integral from 1 to 4 of |x^2-2x-15| is 39

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integral from 1 to 4 of |x^2-2x-15|

\int_{1}^{4} x^{2} - 2 x - 15 d x

39

Solution steps

\int_{1}^{4} x^{2} - 2 x - 15 d x

Eliminate Absolutes

= \int_{1}^{4} - x^{2} + 2 x + 15 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{1}^{4} x^{2} d x + \int_{1}^{4} 2 x d x + \int_{1}^{4} 15 d x

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} 15 d x = 45

= - 21 + 15 + 45

Simplify

= 39

What is the integral from 1 to 4 of |x^2-2x-15| ?
The integral from 1 to 4 of |x^2-2x-15| is 39