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

The integral from 0 to 1 of x+3/2 y^2 is x+1/2

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integral from 0 to 1 of x+3/2 y^2

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

x + \frac{1}{2}

Solution steps

\int_{0}^{1} x + \frac{3}{2} y^{2} 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

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

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

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

= x + \frac{1}{2}

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What is the integral from 0 to 1 of x+3/2 y^2 ?
The integral from 0 to 1 of x+3/2 y^2 is x+1/2