What is the integral from 0 to a of 1-(x^2)/(a^2) ?

The integral from 0 to a of 1-(x^2)/(a^2) is a-a/3

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integral from 0 to a of 1-(x^2)/(a^2)

\int_{0}^{a} 1 - \frac{x ^{2}}{a ^{2}} d x

a - \frac{a}{3}

Solution steps

\int_{0}^{a} 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_{0}^{a} 1 d x - \int_{0}^{a} \frac{x ^{2}}{a ^{2}} d x

\int_{0}^{a} 1 d x = a

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

= a - \frac{a}{3}

\int_{0}^{2} π (4 y^{2} - y^{4}) d y

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

\int_{0}^{6} 4 - 2 x d x

\int_{0}^{1} x^{- 4} d x

\int_{0}^{6} \frac{1}{( 4 - x )} d x

What is the integral from 0 to a of 1-(x^2)/(a^2) ?
The integral from 0 to a of 1-(x^2)/(a^2) is a-a/3