What is the integral from 0 to 4 of 8+2sqrt(x) ?

The integral from 0 to 4 of 8+2sqrt(x) is 128/3

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integral from 0 to 4 of 8+2sqrt(x)

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

\frac{128}{3}

Decimal Notation

42.66666 \dots

Solution steps

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

\int_{0}^{4} 8 d x = 32

\int_{0}^{4} 2 x d x = \frac{32}{3}

= 32 + \frac{32}{3}

Simplify

32 + \frac{32}{3} : \frac{128}{3}

= \frac{128}{3}

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What is the integral from 0 to 4 of 8+2sqrt(x) ?
The integral from 0 to 4 of 8+2sqrt(x) is 128/3