What is the integral from 0 to 1 of sqrt(4x+7) ?

The integral from 0 to 1 of sqrt(4x+7) is (11sqrt(11)-7sqrt(7))/6

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integral from 0 to 1 of sqrt(4x+7)

\int_{0}^{1} 4 x + 7 d x

\frac{11 11 - 7 7}{6}

Decimal

2.99376 \dots

Solution steps

\int_{0}^{1} 4 x + 7 d x

Apply u-substitution

= \int_{7}^{11} \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_{7}^{11} u d u

Apply the Power Rule

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{11}

Compute the boundaries:

\frac{22 11 - 14 7}{3}

= \frac{1}{4} \cdot \frac{22 11 - 14 7}{3}

Simplify

= \frac{11 11 - 7 7}{6}

What is the integral from 0 to 1 of sqrt(4x+7) ?
The integral from 0 to 1 of sqrt(4x+7) is (11sqrt(11)-7sqrt(7))/6