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Anything raised to the zeroth power is a difficult thing to get your head around. The easiest explanation (not a full proof) is to look at what happens as we go down in powers of n: n^3=nnn      ...

This is because you are doubling both the length of the rectangle and its width. If it were extended by a factor of 2 in only one direction then its are would be 2A. Extending it in the other dir...

When you evaluate a definite integral, we can think about using the "+C" and see what happens. Let's take (INT)2x dx between 2 and 3. We then have [x²+C] between 2 and 3. For x=3 we h...

Differentiate x = u² to get dx = 2u du. We need to change the limits, too:

1 <= x <= 9  <==>  1 <= u² <= 9  <==>  1 <= u <= 3  (since we are give...