What is the integral from-4 to 2 of sqrt(17+4x) ?

The integral from-4 to 2 of sqrt(17+4x) is 62/3

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integral from-4 to 2 of sqrt(17+4x)

\int_{- 4}^{2} 17 + 4 x d x

\frac{62}{3}

Decimal

20.66666 \dots

Solution steps

\int_{- 4}^{2} 17 + 4 x d x

Apply u-substitution

: \int_{1}^{25} \frac{u}{4} d u

= \int_{1}^{25} \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_{1}^{25} u d u

Apply the Power Rule

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

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Compute the boundaries:

\frac{248}{3}

= \frac{1}{4} \cdot \frac{248}{3}

Simplify

= \frac{62}{3}

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What is the integral from-4 to 2 of sqrt(17+4x) ?
The integral from-4 to 2 of sqrt(17+4x) is 62/3