What is the integral from 5 to 7 of 2x ?

The integral from 5 to 7 of 2x is 24

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integral from 5 to 7 of 2x

\int_{5}^{7} 2 x d x

24

Solution steps

\int_{5}^{7} 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_{5}^{7} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{5}^{7}

= 2 [\frac{x ^{2}}{2}]_{5}^{7}

Compute the boundaries:

12

= 2 \cdot 12

Simplify

= 24

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