If for n-dimensions f>=0 , prove the integral of f >=0

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Homework Statement



1j9DZU8.png

Homework Equations

The Attempt at a Solution


a) The furthest I have got to understanding the solution is that I need to find a way to show that sup(f(x1,x2,...,xn) >= 0. Intuitively and graphically I can see why the statement is obvious, I'm just having a hard time starting to write the proof...
 
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gradivcurl said:

Homework Statement



1j9DZU8.png

Homework Equations

The Attempt at a Solution


a) The furthest I have got to understanding the solution is that I need to find a way to show that sup(f(x1,x2,...,xn) >= 0. Intuitively and graphically I can see why the statement is obvious, I'm just having a hard time starting to write the proof...

If ##f(x_1,..x_n) \ge 0## then it's pretty obvious ##sup(f(x_1,..x_n)) \ge 0##. If you don't have a convenient theorem like if ##f \ge g## then ##\int f \ge \int g##, then you might have to use the definition of the integral.
 

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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