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

1 Answer
Lovecraft
Sep 18, 2015

#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#

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