What is the integral from 3 to 6 of 2x ?

The integral from 3 to 6 of 2x is 27

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integral from 3 to 6 of 2x

\int_{3}^{6} 2 x d x

27

Solution steps

\int_{3}^{6} 2 x d x

Take the constant out:

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

= 2 \cdot \int_{3}^{6} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{27}{2}

= 2 \cdot \frac{27}{2}

Simplify

= 27

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