What is the integral from p to a+p of x ?

The integral from p to a+p of x is (a^2+2pa)/2

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integral from p to a+p of x

\int_{p}^{a + p} x d x

\frac{a ^{2} + 2 p a}{2}

Solution steps

\int_{p}^{a + p} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{p}^{a + p}

= [\frac{x ^{2}}{2}]_{p}^{a + p}

Compute the boundaries:

\frac{( a + p ) ^{2}}{2} - \frac{p ^{2}}{2}

= \frac{( a + p ) ^{2}}{2} - \frac{p ^{2}}{2}

Simplify

= \frac{a ^{2} + 2 p a}{2}

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What is the integral from p to a+p of x ?
The integral from p to a+p of x is (a^2+2pa)/2