What is the integral from 0 to 5 of (75-3x^2) ?

The integral from 0 to 5 of (75-3x^2) is 250

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integral from 0 to 5 of (75-3x^2)

\int_{0}^{5} (75 - 3 x^{2}) d x

250

Solution steps

\int_{0}^{5} 75 - 3 x^{2} 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} 75 d x - \int_{0}^{5} 3 x^{2} d x

\int_{0}^{5} 75 d x = 375

\int_{0}^{5} 3 x^{2} d x = 125

= 375 - 125

Simplify

= 250

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What is the integral from 0 to 5 of (75-3x^2) ?
The integral from 0 to 5 of (75-3x^2) is 250