Convolution area property derivation

mafra
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Homework Statement


Let y(t) be the convolution of x(t) with h(t), show that the area under y(t) is the product of the areas under x(t) and h(t)

Homework Equations


Convolution definition

The Attempt at a Solution


I found a derivation but it skips a step, uploaded it here:
htt p://i50.tiny pic.com/s15dus.jpg
 
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What's the step that you were wondering about?

s15dus.jpg
 
I don't get how it is possible to separate the integrals in "exchanging the order of integration"
 

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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