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

\int_{0}^{4} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

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\int_{- 1}^{1} \frac{5}{1 + 25 x ^{2}} d x

\int_{y}^{y^{2}} (x + 2 y) d x

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