What is the integral from 1 to 3 of 5x ?

The integral from 1 to 3 of 5x is 20

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integral from 1 to 3 of 5x

\int_{1}^{3} 5 x d x

20

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

4

= 5 \cdot 4

Simplify

= 20

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