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

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

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

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

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

Solution steps

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

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

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

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

\int_{0}^{2} x^{2} + 3 d x

\int_{1}^{3} x^{2} + 2 x - 4 d x

\int_{0}^{1} x^{0} ln (x) d x

\int_{- 1}^{4} \frac{1}{4 - x} d x

\int_{0}^{\frac{π}{2}} \frac{1}{2 + cos ( x )} d x

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