What is the integral from-1 to 8 of (-x^2+10x) ?

The integral from-1 to 8 of (-x^2+10x) is 144

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integral from-1 to 8 of (-x^2+10x)

\int_{- 1}^{8} (- x^{2} + 10 x) d x

144

Solution steps

\int_{- 1}^{8} - x^{2} + 10 x 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}^{8} x^{2} d x + \int_{- 1}^{8} 10 x d x

\int_{- 1}^{8} x^{2} d x = 171

\int_{- 1}^{8} 10 x d x = 315

= - 171 + 315

Simplify

= 144

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What is the integral from-1 to 8 of (-x^2+10x) ?
The integral from-1 to 8 of (-x^2+10x) is 144