What is the integral of 1-(x^2)/(a^2) ?

The integral of 1-(x^2)/(a^2) is x-(x^3)/(3a^2)+C

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integral of 1-(x^2)/(a^2)

\int 1 - \frac{x ^{2}}{a ^{2}} d x

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

Solution steps

\int 1 - \frac{x ^{2}}{a ^{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 1 d x - \int \frac{x ^{2}}{a ^{2}} d x

\int 1 d x = x

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

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

Add a constant to the solution

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

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What is the integral of 1-(x^2)/(a^2) ?
The integral of 1-(x^2)/(a^2) is x-(x^3)/(3a^2)+C