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(Solved): In Exercises 5-7, find positive numbers a and b so that the change of coordinates s=ax,t=by transfo ...
In Exercises 5-7, find positive numbers a and b so that the change of coordinates s=ax,t=by transforms the integral ∬Rdxdy into ∬T∣∣∂(s,t)∂(x,y)∣∣dsdt for the given regions R and T.
7. R is the rectangle 0≤x≤50,0≤y≤10 and T is the square 0≤s,t≤1.
Let us consider the given problem:Now, we are to find the positive numbers and so that change of coordinates transforms the given integrals in the desired form.Given the rectangle is such that and , and the square is such that .