What is the integral from 1 to 5 of 6x ?

The integral from 1 to 5 of 6x is 72

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integral from 1 to 5 of 6x

\int_{1}^{5} 6 x d x

72

Solution steps

\int_{1}^{5} 6 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{1}^{5} x d x

Apply the Power Rule

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

= 6 [\frac{x ^{2}}{2}]_{1}^{5}

Compute the boundaries:

12

= 6 \cdot 12

Simplify

= 72

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