The discussion focuses on reducing a double integral of the form ∫∫dxdyf(x*y) over the triangular region defined by x+y≤1. A key method presented involves changing the inner variable from y to w using the substitution w=xy, which leads to the transformed integral ∫0^1(1/x)∫0^(x-x^2)f(w)dw dx. This approach effectively simplifies the evaluation of the integral by leveraging the dependency of the function on the product x*y.
PREREQUISITESMathematicians, calculus students, and anyone involved in advanced integration techniques, particularly those working with double integrals and variable substitutions.
VytautasD said:I meet with a triangle integral where x+y≤1, and function is dependent only on x*y. I am wondering if there any possibility to relate ∫∫dxdyf(x*y)=∫d(x*y)f(x*y)g(x*y) or something similar? Or maybe there are some assumptions needed to relate like this?