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

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

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

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

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

Solution steps

\int \frac{a ^{2} - 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 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

= \frac{1}{2} (\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}

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

Add a constant to the solution

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

f (x) = \frac{x + 1810}{70 ( x + 2 )}

\int x^{2} - 6 x + 13 d x

x^{2} \frac{d y}{d x} - 2 x y = 4 y^{4}

\int t^{2} e^{- 11 t} d t

x \to 2 lim (3^{x + 1})

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