What is the integral from 0 to 3 of 1/27 (x+y) ?

The integral from 0 to 3 of 1/27 (x+y) is (2x+3)/(18)

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integral from 0 to 3 of 1/27 (x+y)

\int_{0}^{3} \frac{1}{27} (x + y) d y

\frac{2 x + 3}{18}

Solution steps

\int_{0}^{3} \frac{1}{27} (x + y) d y

Take the constant out:

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

= \frac{1}{27} \cdot \int_{0}^{3} x + y d y

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}{27} (\int_{0}^{3} x d y + \int_{0}^{3} y d y)

\int_{0}^{3} x d y = 3 x

\int_{0}^{3} y d y = \frac{9}{2}

= \frac{1}{27} (3 x + \frac{9}{2})

Simplify

\frac{1}{27} (3 x + \frac{9}{2}) : \frac{2 x + 3}{18}

= \frac{2 x + 3}{18}

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What is the integral from 0 to 3 of 1/27 (x+y) ?
The integral from 0 to 3 of 1/27 (x+y) is (2x+3)/(18)