What is the integral from 3 to 5 of 6x ?

The integral from 3 to 5 of 6x is 48

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integral from 3 to 5 of 6x

\int_{3}^{5} 6 x d x

48

Solution steps

\int_{3}^{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_{3}^{5} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{3}^{5}

= 6 [\frac{x ^{2}}{2}]_{3}^{5}

Compute the boundaries:

8

= 6 \cdot 8

Simplify

= 48

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