What is the integral from y to y+1 of (x+y) ?

The integral from y to y+1 of (x+y) is y+(1+2y)/2

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integral from y to y+1 of (x+y)

\int_{y}^{y + 1} (x + y) d x

y + \frac{1 + 2 y}{2}

Solution steps

\int_{y}^{y + 1} x + y 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

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

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

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

= y + \frac{1 + 2 y}{2}

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