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

The integral from 1/2 to 1 of 2x is 3/4

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integral from 1/2 to 1 of 2x

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

\frac{3}{4}

Decimal

0.75

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{3}{8}

= 2 \cdot \frac{3}{8}

Simplify

= \frac{3}{4}

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What is the integral from 1/2 to 1 of 2x ?
The integral from 1/2 to 1 of 2x is 3/4