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

The integral from 1/2 to 3/4 of 2x is 5/16

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

\int_{\frac{1}{2}}^{\frac{3}{4}} 2 x d x

\frac{5}{16}

Decimal

0.3125

Solution steps

\int_{\frac{1}{2}}^{\frac{3}{4}} 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}}^{\frac{3}{4}} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{\frac{1}{2}}^{\frac{3}{4}}

= 2 [\frac{x ^{2}}{2}]_{\frac{1}{2}}^{\frac{3}{4}}

Compute the boundaries:

\frac{5}{32}

= 2 \cdot \frac{5}{32}

Simplify

= \frac{5}{16}

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What is the integral from 1/2 to 3/4 of 2x ?
The integral from 1/2 to 3/4 of 2x is 5/16