What is the integral from a to 2a of (a+x) ?

The integral from a to 2a of (a+x) is 3a^2-(a^2)/2

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integral from a to 2a of (a+x)

\int_{a}^{2 a} (a + x) d x

3 a^{2} - \frac{a ^{2}}{2}

Solution steps

\int_{a}^{2 a} a + 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

= \int_{a}^{2 a} a d x + \int_{a}^{2 a} x d x

\int_{a}^{2 a} a d x = a^{2}

\int_{a}^{2 a} x d x = 2 a^{2} - \frac{a ^{2}}{2}

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

Simplify

= 3 a^{2} - \frac{a ^{2}}{2}

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What is the integral from a to 2a of (a+x) ?
The integral from a to 2a of (a+x) is 3a^2-(a^2)/2