Integrating a polynomial with a square root

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1. Integrate the following: (4x - x^2)^1/2 dx 2. Any assistance would be appreciated.3. Honestly don't know where to start.
 
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Complete the square under the root, and use a trig substitution.
 
Read up on trig substitution. I hadn't covered it yet. Thank you. Works like a charm.
 
Well done.
 

Thread 'Finding the nth roots of a complex number'

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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