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SSC Pure Mathematics QUESTION #1284
Question 1
The contour integral \(\oint_C f(Z)\,dZ\) where \(C\) is a simple closed contour and \(f\) is analytic everywhere inside and on \(C\) equals:
  • 1
  • 2\(\pi i\)
  • \(\pi i\)
Correct Answer Explanation
Cauchy's Integral Theorem states that if \(f\) is analytic on and inside a simple closed contour \(C\), then \(\oint_C f(Z)\,dZ=0\). This is a fundamental result in complex analysis.