GATE 2011 CS (CS1) – Question 41
For $i=\sqrt{-1}$, evaluate $\int_0^{\pi/2}\frac{\cos x+i\sin x}{\cos x-i\sin x}\,dx$.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) i
Explanation
Euler’s identity rewrites the ratio as eⁱˣ/e⁻ⁱˣ=e²ⁱˣ. Integrate to $[e^{2ix}/(2i)]_0^{\pi/2}=(-1-1)/(2i)=-1/i=i$. Thus D.