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## Homework Statement

As part of a bigger problem, I am trying to find the area under the curve

f(x) = sqrt{2x - x

^{2}} between x = 0 and x = 2. To do this, I have to find the antiderivative of f(x)

## Homework Equations

antiderivative

f(x) = ax

^{b}

F(x) = a/(b+1) * x

^{b+1}

chain rule

f(x) = a(b(x))

f'(x) = b'(x) * a'(b(x))

## The Attempt at a Solution

I took the derivative of the terms in the parenthesis, then what was outside the parenthesis, to get

2/3 * (x

^{2}- x

^{3}/3)

^{3/2}

I don't think this is right, because you can use the chain rule to find the derivative, and it's not the original function.

NOTE- I'm not actually old enough and am not actual in a calculus course right now, but I figure that the homework forum would be the best place to put this. Also, don't give me answer, but rather gove me a direction to go in.

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