What is the integral from 0 to 4 of (2+6sqrt(x)) ?

The integral from 0 to 4 of (2+6sqrt(x)) is 40

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integral from 0 to 4 of (2+6sqrt(x))

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

40

Solution steps

\int_{0}^{4} 2 + 6 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} 2 d x + \int_{0}^{4} 6 x d x

\int_{0}^{4} 2 d x = 8

\int_{0}^{4} 6 x d x = 32

= 8 + 32

Simplify

= 40

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What is the integral from 0 to 4 of (2+6sqrt(x)) ?
The integral from 0 to 4 of (2+6sqrt(x)) is 40