Having troubl with this integration

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Homework Statement



Integrate 4X * sqrt( 4-X^2) dX from [-sqrt(2), sqrt(2)]


Homework Equations


Should I use integration by parts?



The Attempt at a Solution

 
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Trig sub should work
 
Neither integration by parts nor a trig substitution. Let u= 4- x^2.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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