What is the integral from 1 to 4 of (3sqrt(x)) ?

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

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integral from 1 to 4 of (3sqrt(x))

\int_{1}^{4} (3 x) d x

14

Solution steps

\int_{1}^{4} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{1}^{4} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{14}{3}

= 3 \cdot \frac{14}{3}

Simplify

= 14

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