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

The integral from 0 to 4 of (2x+sqrt(x)) is 64/3

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

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

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

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

\int_{0}^{4} 2 x d x = 16

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

= 16 + \frac{16}{3}

Simplify

16 + \frac{16}{3} : \frac{64}{3}

= \frac{64}{3}

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What is the integral from 0 to 4 of (2x+sqrt(x)) ?
The integral from 0 to 4 of (2x+sqrt(x)) is 64/3