What is the integral from 0 to 1 of sqrt(2x+7) ?

The integral from 0 to 1 of sqrt(2x+7) is (27-7sqrt(7))/3

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integral from 0 to 1 of sqrt(2x+7)

\int_{0}^{1} 2 x + 7 d x

\frac{27 - 7 7}{3}

Decimal

2.82658 \dots

Solution steps

\int_{0}^{1} 2 x + 7 d x

Apply u-substitution

: \int_{7}^{9} \frac{u}{2} d u

= \int_{7}^{9} \frac{u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{7}^{9} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{9}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{9}

Compute the boundaries:

18 - \frac{14 7}{3}

= \frac{1}{2} (18 - \frac{14 7}{3})

Simplify

= \frac{27 - 7 7}{3}

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What is the integral from 0 to 1 of sqrt(2x+7) ?
The integral from 0 to 1 of sqrt(2x+7) is (27-7sqrt(7))/3