1zero
12 Answers
39the indefinite integral is
(1/2) (x + ln| sin x + cos x |)
evaluating it between 0 and pi u get pi/2 as the answer
39http://in.answers.yahoo.com/question/index?qid=20100421045250AAFKPYc
341\int_0^{\pi} \frac{dx}{1+\tan x} = \frac{1}{2} \int_0^{\pi} 1 + \frac{1-\tan x}{1+ \tan x} \ dx= \frac{\pi}{2} + \frac{1}{2} \int_0^{\pi} \tan \left(\frac{\pi}{4}-x \right) \ dx
\int_0^{\pi} \tan \left(\frac{\pi}{4}-x \right) \ dx = \int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \tan y \ dy = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cot y \ dy = 0
Hence the integral evaluates to
\frac{\pi}{2}
1but tan x is discontinous at π/2,we have to break the limits in the last step
39lol! Would you believe it....the Yahoo Answers page !^--_--^! posted...the second answer on it is by me xD
341@redox - not if you are invoking a result about integral of an odd function about an interval symmetric about x=0.