What is the integral from 1 to 7 of 2x ?

The integral from 1 to 7 of 2x is 48

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integral from 1 to 7 of 2x

\int_{1}^{7} 2 x d x

48

Solution steps

\int_{1}^{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_{1}^{7} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{1}^{7}

= 2 [\frac{x ^{2}}{2}]_{1}^{7}

Compute the boundaries:

24

= 2 \cdot 24

Simplify

= 48

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