What is the integral from 1 to 6 of x^2-7x+6 ?

The integral from 1 to 6 of x^2-7x+6 is -125/6

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integral from 1 to 6 of x^2-7x+6

\int_{1}^{6} x^{2} - 7 x + 6 d x

- \frac{125}{6}

Decimal

- 20.83333 \dots

Solution steps

\int_{1}^{6} x^{2} - 7 x + 6 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}^{6} x^{2} d x - \int_{1}^{6} 7 x d x + \int_{1}^{6} 6 d x

\int_{1}^{6} x^{2} d x = \frac{215}{3}

\int_{1}^{6} 7 x d x = \frac{245}{2}

\int_{1}^{6} 6 d x = 30

= \frac{215}{3} - \frac{245}{2} + 30

Simplify

\frac{215}{3} - \frac{245}{2} + 30 : - \frac{125}{6}

= - \frac{125}{6}

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What is the integral from 1 to 6 of x^2-7x+6 ?
The integral from 1 to 6 of x^2-7x+6 is -125/6