What is the integral from 0 to 1 of 2/5 (2x+3y) ?

The integral from 0 to 1 of 2/5 (2x+3y) is 4/5 x+3/5

integral from 0 to 1 of 2/5 (2x+3y)

\int_{0}^{1} \frac{2}{5} (2 x + 3 y) d y

\frac{4}{5} x + \frac{3}{5}

Solution steps

\int_{0}^{1} \frac{2}{5} (2 x + 3 y) d y

Take the constant out:

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

= \frac{2}{5} \cdot \int_{0}^{1} 2 x + 3 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{2}{5} (\int_{0}^{1} 2 x d y + \int_{0}^{1} 3 y d y)

\int_{0}^{1} 2 x d y = 2 x

\int_{0}^{1} 3 y d y = \frac{3}{2}

= \frac{2}{5} (2 x + \frac{3}{2})

Simplify

\frac{2}{5} (2 x + \frac{3}{2}) : \frac{4}{5} x + \frac{3}{5}

= \frac{4}{5} x + \frac{3}{5}

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What is the integral from 0 to 1 of 2/5 (2x+3y) ?
The integral from 0 to 1 of 2/5 (2x+3y) is 4/5 x+3/5