What is the integral from 0 to 1 of ((x+5)/2)^2 ?

The integral from 0 to 1 of ((x+5)/2)^2 is 91/12

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integral from 0 to 1 of ((x+5)/2)^2

\int_{0}^{1} (\frac{x + 5}{2})^{2} d x

\frac{91}{12}

Decimal Notation

7.58333 \dots

Solution steps

\int_{0}^{1} (\frac{x + 5}{2})^{2} d x

Apply Integration By Parts

: [\frac{1}{4} x (x + 5)^{2} - \int \frac{1}{2} x (x + 5) d x]_{0}^{1}

= [\frac{1}{4} x (x + 5)^{2} - \int \frac{1}{2} x (x + 5) d x]_{0}^{1}

\int \frac{1}{2} x (x + 5) d x = \frac{1}{2} (\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2})

= [\frac{1}{4} x (x + 5)^{2} - \frac{1}{2} (\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2})]_{0}^{1}

Simplify

[\frac{1}{4} x (x + 5)^{2} - \frac{1}{2} (\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2})]_{0}^{1} : [\frac{1}{12} (x^{3} + 15 x^{2} + 75 x)]_{0}^{1}

= [\frac{1}{12} (x^{3} + 15 x^{2} + 75 x)]_{0}^{1}

Compute the boundaries:

\frac{91}{12}

= \frac{91}{12}

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What is the integral from 0 to 1 of ((x+5)/2)^2 ?
The integral from 0 to 1 of ((x+5)/2)^2 is 91/12