What is the integral from 1 to 7 of (x^2-4x-12) ?

The integral from 1 to 7 of (x^2-4x-12) is -54

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integral from 1 to 7 of (x^2-4x-12)

\int_{1}^{7} (x^{2} - 4 x - 12) d x

- 54

Solution steps

\int_{1}^{7} x^{2} - 4 x - 12 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}^{7} x^{2} d x - \int_{1}^{7} 4 x d x - \int_{1}^{7} 12 d x

\int_{1}^{7} x^{2} d x = 114

\int_{1}^{7} 4 x d x = 96

\int_{1}^{7} 12 d x = 72

= 114 - 96 - 72

Simplify

= - 54

What is the integral from 1 to 7 of (x^2-4x-12) ?
The integral from 1 to 7 of (x^2-4x-12) is -54