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

The integral from 1 to 6 of 6x is 105

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integral from 1 to 6 of 6x

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

105

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{35}{2}

= 6 \cdot \frac{35}{2}

Simplify

= 105

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