What is the integral from 1/4 to 1/2 of (2(x+2))/5 ?

The integral from 1/4 to 1/2 of (2(x+2))/5 is 19/80

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integral from 1/4 to 1/2 of (2(x+2))/5

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{2 ( x + 2 )}{5} d x

\frac{19}{80}

Decimal

0.2375

Solution steps

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{2 ( x + 2 )}{5} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{5} \cdot \int_{\frac{1}{4}}^{\frac{1}{2}} x + 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{2}{5} (\int_{\frac{1}{4}}^{\frac{1}{2}} x d x + \int_{\frac{1}{4}}^{\frac{1}{2}} 2 d x)

\int_{\frac{1}{4}}^{\frac{1}{2}} x d x = \frac{3}{32}

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

= \frac{2}{5} (\frac{3}{32} + \frac{1}{2})

Simplify

\frac{2}{5} (\frac{3}{32} + \frac{1}{2}) : \frac{19}{80}

= \frac{19}{80}

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What is the integral from 1/4 to 1/2 of (2(x+2))/5 ?
The integral from 1/4 to 1/2 of (2(x+2))/5 is 19/80