What is the integral from 0 to 9 of 3sqrt(x) ?

The integral from 0 to 9 of 3sqrt(x) is 54

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integral from 0 to 9 of 3sqrt(x)

\int_{0}^{9} 3 x d x

54

Solution steps

\int_{0}^{9} 3 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{9} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{9}

= 3 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{9}

Compute the boundaries:

18

= 3 \cdot 18

Simplify

= 54

\int_{0}^{\frac{1}{2}} \frac{1}{1 + x ^{3}} d x

\int_{0}^{1} 3 r^{2} e^{r^{3}} d r

\int_{2}^{5} 2 x^{2} d x

\int_{- 1}^{1} \frac{x}{5 - 4 x} d x

\int_{1}^{3} \frac{x - 1}{x} d x

What is the integral from 0 to 9 of 3sqrt(x) ?
The integral from 0 to 9 of 3sqrt(x) is 54