What is the integral from 0 to 4 of 9+2sqrt(x) ?

The integral from 0 to 4 of 9+2sqrt(x) is 140/3

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integral from 0 to 4 of 9+2sqrt(x)

\int_{0}^{4} 9 + 2 x d x

\frac{140}{3}

Decimal

46.66666 \dots

Solution steps

\int_{0}^{4} 9 + 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} 9 d x + \int_{0}^{4} 2 x d x

\int_{0}^{4} 9 d x = 36

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

= 36 + \frac{32}{3}

Simplify

36 + \frac{32}{3} : \frac{140}{3}

= \frac{140}{3}

What is the integral from 0 to 4 of 9+2sqrt(x) ?
The integral from 0 to 4 of 9+2sqrt(x) is 140/3