Evaluate the following integrals by computing residues at infinity. Check your answers by computing residues at all the finite poles. (It is understood that ∮ means in the positive direction.) ∮ 1 − z 2 1 + z 2 d z z around | z | = 2.
Evaluate the following integrals by computing residues at infinity. Check your answers by computing residues at all the finite poles. (It is understood that ∮ means in the positive direction.) ∮ 1 − z 2 1 + z 2 d z z around | z | = 2.
Evaluate the following integrals by computing residues at infinity. Check your answers by computing residues at all the finite poles. (It is understood that
∮
means in the positive direction.)
∮
1
−
z
2
1
+
z
2
d
z
z
around
|
z
|
=
2.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Q2. Using the complex variables techniques, evaluate the integral dx
For each of following equations find the general integral and compute three different solutions. Describe the
domain(s) of the (x.y)-plane in which each these solutions is defined.
(b) zzz + yzy
(c) a² zr + y² zy = (x + y)z
Use U-Substitution to evaluate the definite integrals.
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