Residues / Integrals - Complex Analysis : integral from 0 to pi/2 of ( d theta/ ( a + sin^2 theta) ) = pi/2[a(a+1)]^1/2 if a > 0.
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Verify the following equation:
integral from 0 to pi/2 of ( d theta/ ( a + sin^2 theta) ) = pi/2[a(a+1)]^1/2 if a > 0.
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Residue Theory
Many real integrals can be evaluated using integration within the complex plane using the astonishing result that:
That is, integrating f(z) around a closed loop in the complex plane results in a value which is the same summing the residues of f(z) at all the poles within the loop.
If ...
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