What is the integral from 1 to 9 of-x^2+10x-9 ?

The integral from 1 to 9 of-x^2+10x-9 is 256/3

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integral from 1 to 9 of-x^2+10x-9

\int_{1}^{9} - x^{2} + 10 x - 9 d x

\frac{256}{3}

Decimal Notation

85.33333 \dots

Solution steps

\int_{1}^{9} - x^{2} + 10 x - 9 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}^{9} x^{2} d x + \int_{1}^{9} 10 x d x - \int_{1}^{9} 9 d x

\int_{1}^{9} x^{2} d x = \frac{728}{3}

\int_{1}^{9} 10 x d x = 400

\int_{1}^{9} 9 d x = 72

= - \frac{728}{3} + 400 - 72

Simplify

- \frac{728}{3} + 400 - 72 : \frac{256}{3}

= \frac{256}{3}

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What is the integral from 1 to 9 of-x^2+10x-9 ?
The integral from 1 to 9 of-x^2+10x-9 is 256/3