What is the integral from 0 to 1 of 12/7 (xy+y^2) ?

The integral from 0 to 1 of 12/7 (xy+y^2) is 12/7 (y^2+y/2)

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integral from 0 to 1 of 12/7 (xy+y^2)

\int_{0}^{1} \frac{12}{7} (x y + y^{2}) d x

\frac{12}{7} (y^{2} + \frac{y}{2})

Solution steps

\int_{0}^{1} \frac{12}{7} (x y + y^{2}) d x

Take the constant out:

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

= \frac{12}{7} \cdot \int_{0}^{1} y^{2} + 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{12}{7} (\int_{0}^{1} y^{2} d x + \int_{0}^{1} y x d x)

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

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

= \frac{12}{7} (y^{2} + \frac{y}{2})

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What is the integral from 0 to 1 of 12/7 (xy+y^2) ?
The integral from 0 to 1 of 12/7 (xy+y^2) is 12/7 (y^2+y/2)