What is the integral from 0 to a of (ax^2-x^3) ?

The integral from 0 to a of (ax^2-x^3) is (a^4)/3-(a^4)/4

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integral from 0 to a of (ax^2-x^3)

\int_{0}^{a} (a x^{2} - x^{3}) d x

\frac{a ^{4}}{3} - \frac{a ^{4}}{4}

Solution steps

\int_{0}^{a} a x^{2} - x^{3} 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 x^{2} d x - \int_{0}^{a} x^{3} d x

\int_{0}^{a} a x^{2} d x = \frac{a ^{4}}{3}

\int_{0}^{a} x^{3} d x = \frac{a ^{4}}{4}

= \frac{a ^{4}}{3} - \frac{a ^{4}}{4}

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What is the integral from 0 to a of (ax^2-x^3) ?
The integral from 0 to a of (ax^2-x^3) is (a^4)/3-(a^4)/4