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

The integral from 0 to 1 of (sqrt(1+7x)) is (32sqrt(2)-2)/(21)

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

\int_{0}^{1} (1 + 7 x) d x

\frac{32 2 - 2}{21}

Decimal

2.05975 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{8} \frac{u}{7} d u

= \int_{1}^{8} \frac{u}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{1}^{8} u d u

Apply the Power Rule

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

= \frac{1}{7} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{8}

Compute the boundaries:

\frac{32 2}{3} - \frac{2}{3}

= \frac{1}{7} (\frac{32 2}{3} - \frac{2}{3})

Simplify

= \frac{32 2 - 2}{21}

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What is the integral from 0 to 1 of (sqrt(1+7x)) ?
The integral from 0 to 1 of (sqrt(1+7x)) is (32sqrt(2)-2)/(21)