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

The integral from 1 to 4 of 5x is 75/2

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integral from 1 to 4 of 5x

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

\frac{75}{2}

Solution steps

\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{x ^{2}}{2}]_{1}^{4}

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

Compute the boundaries:

\frac{15}{2}

= 5 \cdot \frac{15}{2}

Simplify

= \frac{75}{2}

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