What is the integral from 0 to 9 of-x^2+18x-x^2 ?

The integral from 0 to 9 of-x^2+18x-x^2 is 243

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integral from 0 to 9 of-x^2+18x-x^2

\int_{0}^{9} - x^{2} + 18 x - x^{2} d x

243

Solution steps

\int_{0}^{9} - x^{2} + 18 x - x^{2} d x

Simplify

= \int_{0}^{9} - 2 x^{2} + 18 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_{0}^{9} 2 x^{2} d x + \int_{0}^{9} 18 x d x

\int_{0}^{9} 2 x^{2} d x = 486

\int_{0}^{9} 18 x d x = 729

= - 486 + 729

Simplify

= 243

\int_{4}^{9} (\frac{1}{x}) d x

\int_{- 1}^{1} x^{2} + 2 x - 3 d x

\int_{0}^{6} (x^{2} - 3 x + 4) d x

\int_{1}^{6} x^{3} ln (x) d x

\int_{2}^{6} 6 x - 18 d x

What is the integral from 0 to 9 of-x^2+18x-x^2 ?
The integral from 0 to 9 of-x^2+18x-x^2 is 243