What is the integral from 0 to 6 of sqrt(3x+7) ?

The integral from 0 to 6 of sqrt(3x+7) is (250-14sqrt(7))/9

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integral from 0 to 6 of sqrt(3x+7)

\int_{0}^{6} 3 x + 7 d x

\frac{250 - 14 7}{9}

Decimal Notation

23.66216 \dots

Solution steps

\int_{0}^{6} 3 x + 7 d x

Apply u-substitution

: \int_{7}^{25} \frac{u}{3} d u

= \int_{7}^{25} \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{7}^{25} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{25}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{25}

Compute the boundaries:

\frac{250}{3} - \frac{14 7}{3}

= \frac{1}{3} (\frac{250}{3} - \frac{14 7}{3})

Simplify

= \frac{250 - 14 7}{9}

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What is the integral from 0 to 6 of sqrt(3x+7) ?
The integral from 0 to 6 of sqrt(3x+7) is (250-14sqrt(7))/9