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

The integral from 1 to 5 of 5x is 60

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integral from 1 to 5 of 5x

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

60

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

12

= 5 \cdot 12

Simplify

= 60

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