What is the integral from 1 to 2 of (2x) ?

The integral from 1 to 2 of (2x) is 3

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integral from 1 to 2 of (2x)

\int_{1}^{2} (2 x) d x

3

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{3}{2}

= 2 \cdot \frac{3}{2}

Simplify

= 3

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What is the integral from 1 to 2 of (2x) ?
The integral from 1 to 2 of (2x) is 3