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

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

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integral of (1-x^2)/2

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

\frac{1}{2} (x - \frac{x ^{3}}{3}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 - 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

= \frac{1}{2} (\int 1 d x - \int x^{2} d x)

\int 1 d x = x

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

= \frac{1}{2} (x - \frac{x ^{3}}{3})

Add a constant to the solution

= \frac{1}{2} (x - \frac{x ^{3}}{3}) + C

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