What is the integral from 1 to 4 of sqrt(5x) ?

The integral from 1 to 4 of sqrt(5x) is (14sqrt(5))/3

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integral from 1 to 4 of sqrt(5x)

\int_{1}^{4} 5 x d x

\frac{14 5}{3}

Solution steps

\int_{1}^{4} 5 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int_{1}^{4} 5 x d x

Take the constant out:

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

= 5 \cdot \int_{1}^{4} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

= 5 [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

\frac{14}{3}

= 5 \frac{14}{3}

Simplify

= \frac{14 5}{3}

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What is the integral from 1 to 4 of sqrt(5x) ?
The integral from 1 to 4 of sqrt(5x) is (14sqrt(5))/3