What is the integral from 0 to 5 of (x+y)/(55) ?

The integral from 0 to 5 of (x+y)/(55) is (2y+5)/(22)

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integral from 0 to 5 of (x+y)/(55)

\int_{0}^{5} \frac{x + y}{55} d x

\frac{2 y + 5}{22}

Solution steps

\int_{0}^{5} \frac{x + y}{55} d x

Take the constant out:

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

= \frac{1}{55} \cdot \int_{0}^{5} y + x 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{1}{55} (\int_{0}^{5} y d x + \int_{0}^{5} x d x)

\int_{0}^{5} y d x = 5 y

\int_{0}^{5} x d x = \frac{25}{2}

= \frac{1}{55} (5 y + \frac{25}{2})

Simplify

\frac{1}{55} (5 y + \frac{25}{2}) : \frac{2 y + 5}{22}

= \frac{2 y + 5}{22}

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What is the integral from 0 to 5 of (x+y)/(55) ?
The integral from 0 to 5 of (x+y)/(55) is (2y+5)/(22)