Evaluate:
where a and b are positive real numbers. (Here max(s,t) is defined as the larger of the two numbers s and t.)
how do i even begin this? I am not familiar with this max(s,t) function, how does one determine which is greater in this case (depends on x and y, right?).
I'm confused as to how switching the order of integration would help.Originally Posted by Prove It
Regardless of the order of integration, doesn'tor
have to be integrated, which I know can't be done with elementary functions and I don't know how to do it.
a^2x^2> b^2y^2, with all numbers positive, if and only if ax/b> y
You will need to break this into two double integrals will. We have x going from 0 to a and, for each x, y going from 0 to b. Instead, do one integral with y going from 0 to ax/b and another with y going from ax/b to b. In the first integral,and in the other
.
Once you have done that, see if changing the order of integration doesn't help.
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