What is the integral from 0 to r of ax^2+bx+c ?

The integral from 0 to r of ax^2+bx+c is (ar^3)/3+(br^2)/2+cr

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integral from 0 to r of ax^2+bx+c

\int_{0}^{r} a x^{2} + b x + c d x

\frac{a r ^{3}}{3} + \frac{b r ^{2}}{2} + cr

Solution steps

\int_{0}^{r} a x^{2} + b x + c 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}^{r} a x^{2} d x + \int_{0}^{r} b x d x + \int_{0}^{r} c d x

\int_{0}^{r} a x^{2} d x = \frac{a r ^{3}}{3}

\int_{0}^{r} b x d x = \frac{b r ^{2}}{2}

\int_{0}^{r} c d x = cr

= \frac{a r ^{3}}{3} + \frac{b r ^{2}}{2} + cr

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What is the integral from 0 to r of ax^2+bx+c ?
The integral from 0 to r of ax^2+bx+c is (ar^3)/3+(br^2)/2+cr