What is the integral of 10000-x^2 ?

The integral of 10000-x^2 is 10000x-(x^3)/3+C

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integral of 10000-x^2

\int 10000 - x^{2} d x

10000 x - \frac{x ^{3}}{3} + C

Solution steps

\int 10000 - 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 10000 d x - \int x^{2} d x

\int 10000 d x = 10000 x

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

= 10000 x - \frac{x ^{3}}{3}

Add a constant to the solution

= 10000 x - \frac{x ^{3}}{3} + C

y = x^{2} - 4 x, y = - 2 x

x \to 2 lim (- 2 x^{2})

4 x^{2}, \frac{1}{4} x

\frac{d}{d x} (tanh (ln (x)))

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

What is the integral of 10000-x^2 ?
The integral of 10000-x^2 is 10000x-(x^3)/3+C