What is the integral from 6 to 7 of x^2-4x-12 ?

The integral from 6 to 7 of x^2-4x-12 is 13/3

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integral from 6 to 7 of x^2-4x-12

\int_{6}^{7} x^{2} - 4 x - 12 d x

\frac{13}{3}

Decimal

4.33333 \dots

Solution steps

\int_{6}^{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_{6}^{7} x^{2} d x - \int_{6}^{7} 4 x d x - \int_{6}^{7} 12 d x

\int_{6}^{7} x^{2} d x = \frac{127}{3}

\int_{6}^{7} 4 x d x = 26

\int_{6}^{7} 12 d x = 12

= \frac{127}{3} - 26 - 12

Simplify

\frac{127}{3} - 26 - 12 : \frac{13}{3}

= \frac{13}{3}

What is the integral from 6 to 7 of x^2-4x-12 ?
The integral from 6 to 7 of x^2-4x-12 is 13/3