engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Complex Variables Cauchy's Integral Theorem
Consider the integral \(\displaystyle\oint_C \dfrac{\sin (x)}{x^2 (x^2 + 4)}dx\)
Where C is a counter-clockwise oriented circle defined as |x - i| = 2. The value of the integral is
1
\(\dfrac{\pi}{4} \sin (2i)\)
2
\(\frac{\pi i}{2}-\dfrac{\pi}{8} \sin (2i)\)
3
\(\dfrac{\pi}{8} \sin (2i)\)
4
\(-\dfrac{\pi}{4} \sin (2i)\)