What is the integral from x/2 to 3-x of x+y ?

The integral from x/2 to 3-x of x+y is x(3-x)-(x^2)/2+(36-24x+3x^2)/8

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integral from x/2 to 3-x of x+y

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

x (3 - x) - \frac{x ^{2}}{2} + \frac{36 - 24 x + 3 x ^{2}}{8}

Solution steps

\int_{\frac{x}{2}}^{3 - x} 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

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

\int_{\frac{x}{2}}^{3 - x} x d y = x (3 - x) - \frac{x ^{2}}{2}

\int_{\frac{x}{2}}^{3 - x} y d y = \frac{36 - 24 x + 3 x ^{2}}{8}

= x (3 - x) - \frac{x ^{2}}{2} + \frac{36 - 24 x + 3 x ^{2}}{8}

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What is the integral from x/2 to 3-x of x+y ?
The integral from x/2 to 3-x of x+y is x(3-x)-(x^2)/2+(36-24x+3x^2)/8