What is the integral from 0 to 5 of 255-(9x^2+2x+20) ?

The integral from 0 to 5 of 255-(9x^2+2x+20) is 775

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integral from 0 to 5 of 255-(9x^2+2x+20)

\int_{0}^{5} 255 - (9 x^{2} + 2 x + 20) d x

775

Solution steps

\int_{0}^{5} 255 - (9 x^{2} + 2 x + 20) d x

Simplify

= \int_{0}^{5} - 9 x^{2} - 2 x + 235 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}^{5} 9 x^{2} d x - \int_{0}^{5} 2 x d x + \int_{0}^{5} 235 d x

\int_{0}^{5} 9 x^{2} d x = 375

\int_{0}^{5} 2 x d x = 25

\int_{0}^{5} 235 d x = 1175

= - 375 - 25 + 1175

Simplify

= 775

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What is the integral from 0 to 5 of 255-(9x^2+2x+20) ?
The integral from 0 to 5 of 255-(9x^2+2x+20) is 775