What is the integral from 0 to 6 of 3x ?

The integral from 0 to 6 of 3x is 54

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integral from 0 to 6 of 3x

\int_{0}^{6} 3 x d x

54

Solution steps

\int_{0}^{6} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{0}^{6} x d x

Apply the Power Rule

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

= 3 [\frac{x ^{2}}{2}]_{0}^{6}

Compute the boundaries:

18

= 3 \cdot 18

Simplify

= 54

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