What is the integral from 0 to 4 of (5x-3sqrt(x)) ?

The integral from 0 to 4 of (5x-3sqrt(x)) is 24

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integral from 0 to 4 of (5x-3sqrt(x))

\int_{0}^{4} (5 x - 3 x) d x

24

Solution steps

\int_{0}^{4} 5 x - 3 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}^{4} 5 x d x - \int_{0}^{4} 3 x d x

\int_{0}^{4} 5 x d x = 40

\int_{0}^{4} 3 x d x = 16

= 40 - 16

Simplify

= 24

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What is the integral from 0 to 4 of (5x-3sqrt(x)) ?
The integral from 0 to 4 of (5x-3sqrt(x)) is 24