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

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

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integral of (a^2-x^2)

\int (a^{2} - x^{2}) d x

a^{2} x - \frac{x ^{3}}{3} + C

Solution steps

\int 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 a^{2} d x - \int x^{2} d x

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

Add a constant to the solution

= a^{2} x - \frac{x ^{3}}{3} + C