Question

How do you find the antiderivative of the `sqrt`4-x^2#?

Answer 1

`int(4-x^2)dx = 4x - x^3/3 + c`

Explanation:

Okay, the antiderivative is nothing more, nothing less than the integral. So:

`int(4-x^2)dx`

The integral of any constant, is itself times the variable whereas the integral of `x^2` is, naturally `x^3/3` because that's the function we derive to get `x^2`, or, because of the formula `x^(n+1)/(n+1)`, whichever you prefer.

So, in the end we have:
`int(4-x^2)dx = 4x - x^3/3 + c`

Whereas `c` is the integrating constant because for any value of `c` that function would still derive to `4-x^2`