What is the integral from 0 to 3 of 3sqrt(8x+1) ?

The integral from 0 to 3 of 3sqrt(8x+1) is 31

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integral from 0 to 3 of 3sqrt(8x+1)

\int_{0}^{3} 3 8 x + 1 d x

31

Solution steps

\int_{0}^{3} 3 8 x + 1 d x

Take the constant out:

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

= 3 \cdot \int_{0}^{3} 8 x + 1 d x

Apply u-substitution

: \int_{1}^{25} \frac{u}{8} d u

= 3 \cdot \int_{1}^{25} \frac{u}{8} d u

Take the constant out:

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

= 3 \cdot \frac{1}{8} \cdot \int_{1}^{25} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

= 3 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Simplify

3 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25} : \frac{3}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

= \frac{3}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Compute the boundaries:

\frac{248}{3}

= \frac{3}{8} \cdot \frac{248}{3}

Simplify

= 31

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What is the integral from 0 to 3 of 3sqrt(8x+1) ?
The integral from 0 to 3 of 3sqrt(8x+1) is 31