What is the integral from 0 to 1 of sqrt(5x+7) ?

The integral from 0 to 1 of sqrt(5x+7) is (48sqrt(3)-14sqrt(7))/(15)

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integral from 0 to 1 of sqrt(5x+7)

\int_{0}^{1} 5 x + 7 d x

\frac{48 3 - 14 7}{15}

Solution steps

\int_{0}^{1} 5 x + 7 d x

Apply u-substitution

: \int_{7}^{12} \frac{u}{5} d u

= \int_{7}^{12} \frac{u}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{7}^{12} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{12}

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{12}

Compute the boundaries:

163 - \frac{14 7}{3}

= \frac{1}{5} (163 - \frac{14 7}{3})

Simplify

= \frac{48 3 - 14 7}{15}

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What is the integral from 0 to 1 of sqrt(5x+7) ?
The integral from 0 to 1 of sqrt(5x+7) is (48sqrt(3)-14sqrt(7))/(15)