What is the integral from 0 to 1 of sqrt(4x+6) ?

The integral from 0 to 1 of sqrt(4x+6) is (5sqrt(10)-3sqrt(6))/3

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integral from 0 to 1 of sqrt(4x+6)

\int_{0}^{1} 4 x + 6 d x

\frac{5 10 - 3 6}{3}

Decimal

2.82097 \dots

Solution steps

\int_{0}^{1} 4 x + 6 d x

Apply u-substitution

: \int_{6}^{10} \frac{u}{4} d u

= \int_{6}^{10} \frac{u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{6}^{10} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{6}^{10}

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{6}^{10}

Compute the boundaries:

\frac{20 10}{3} - 46

= \frac{1}{4} (\frac{20 10}{3} - 46)

Simplify

= \frac{5 10 - 3 6}{3}

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What is the integral from 0 to 1 of sqrt(4x+6) ?
The integral from 0 to 1 of sqrt(4x+6) is (5sqrt(10)-3sqrt(6))/3