What is the integral from 0 to 6 of 5x ?

The integral from 0 to 6 of 5x is 90

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integral from 0 to 6 of 5x

\int_{0}^{6} 5 x d x

90

Solution steps

\int_{0}^{6} 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_{0}^{6} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{6}

= 5 [\frac{x ^{2}}{2}]_{0}^{6}

Compute the boundaries:

18

= 5 \cdot 18

Simplify

= 90

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