What is the integral from 0 to a of (a-x) ?

The integral from 0 to a of (a-x) is a^2-(a^2)/2

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integral from 0 to a of (a-x)

\int_{0}^{a} (a - x) d x

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

Solution steps

\int_{0}^{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_{0}^{a} a d x - \int_{0}^{a} x d x

\int_{0}^{a} a d x = a^{2}

\int_{0}^{a} x d x = \frac{a ^{2}}{2}

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

What is the integral from 0 to a of (a-x) ?
The integral from 0 to a of (a-x) is a^2-(a^2)/2