Evaluate $\int_{-1}^{1} \frac{\sqrt{1-x^2}}{1+x^2}dx$ using the residues.
I am not really sure what contour I should be considering.
2026-04-07 08:19:31.1775549971
Evaluating a definite integral using contour integration
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Hint: Rewrite your integral in terms of trig functions. Your integral is equal to $$ \int_{-\pi/2}^{\pi/2}\frac{\cos^2 t}{1+\sin^2 t}dt $$