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HallsofIvy said:Well, "assembly" isn't the correct English. "Union" of the two sets or "combination" of the two paths woud be better.
In any case, the problem, as I interpret this is to integrate some function from -R to R along the real line, then integrate from R to -R along the upper half circle with radius R. On the left, [itex]\gamma1[/itex] seems to be the line y= x or, in terms of complex numbers, t+ it, for t from -R to R. No, that is not at all what is given. But the picture on the right is not clear. You seem to be indicating that [itex]\gamma1[/itex] is raised up to some non-zero y, or in terms of complex numbers, t+ ai for some positive a. That is also not correct. [itex]\gamma1[/itex] is given as t+0i, not t+ some non-zero number times i. You should be showing [itex]\gamma1[/itex] running on the real axis, not above it.
HallsofIvy said:What you have is correct but this looks more like a problem where you are expected to evaluate the integral around the closed path by using Residues. The integrand has poles of order 1 at i, -i, 2i, and -2i, of which i and 2i are inside the closed path.
"Find the path assembly" is a scientific method that involves identifying and assembling a series of components or steps to reach a desired outcome or solution.
Using "Find the path assembly" allows for a systematic approach to problem-solving and can lead to more efficient and effective solutions. It also encourages critical thinking and creativity in finding the most optimal path.
To use "Find the path assembly", first clearly define the problem or desired outcome. Then, break down the components or steps needed to reach the goal. Finally, assemble the components in the most logical and efficient way to achieve the desired result.
While "Find the path assembly" can be a useful method, it may not always be applicable to every problem or situation. It also relies on accurate and complete information to identify the most optimal path.
Yes, "Find the path assembly" can be used in any field of science as it is a general problem-solving method. It can be applied to a wide range of situations, from basic scientific research to complex engineering problems.