Consider the integral I = int_(0)^(2pi) (dx)/( 5 - 2 cos x) . Making the substitution tan (x)/(2) = t we have int_(0)^(2pi) (dx)/(5 - 2 cos x) = int_(0)^(0) (2 dt)/((1+ t^(2))(5 - 2 (1-t^(2))/(1+ t^(2))))=0 The result isobviouslywrong, since the integrand is positive, and , consequently, theintegral of this function cannot be equal to zero . Find the mistake.

Consider the integral I = int_(0)^(2pi) (dx)/( 5 - 2 cos x) . Making t

1.	Consider the integral I = int_(0)^(2pi) (dx)/( 5 - 2 cos x) . Making the substitution tan (x)/(2) = t we have int_(0)^(2pi) (dx)/(5 - 2 cos x) = int_(0)^(0) (2 dt)/((1+ t^(2))(5 - 2 (1-t^(2))/(1+ t^(2))))=0 The result isobviouslywrong, since the integrand is positive, and , consequently, theintegral of this function cannot be equal to zero . Find the mistake.
Answer» ANSWER :Thesubstitutiont = tan `(x)/(2)` will not do, since thisfunction is discontinuous at `x = PI`

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