What is the integral from 0 to 4 of 3sqrt(x) ?

The integral from 0 to 4 of 3sqrt(x) is 16

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integral from 0 to 4 of 3sqrt(x)

\int_{0}^{4} 3 x d x

16

Solution steps

\int_{0}^{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_{0}^{4} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

= 3 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

Compute the boundaries:

\frac{16}{3}

= 3 \cdot \frac{16}{3}

Simplify

= 16

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\int_{0}^{1} sin^{2} (nπ x) d x

What is the integral from 0 to 4 of 3sqrt(x) ?
The integral from 0 to 4 of 3sqrt(x) is 16