Question

limit 0 to pie sec*2 x / 1 + 2tan*2 x

Answer 1

Answer:

$\huge \mathfrak \red{ \fbox{solution}} \\ \\ \implies \: \:\int\limits_{0}^{ \pi} \frac{ {sec}^{2}x }{1 + 2 {tan}^{2}x } dx \\ \\ let \: \: \: tan \: x = t.....(1) \\ \\ differentiating \: with \: respect \: to \: t \\ \\ {sec}^{2} x.dx = dt \\ \\now \: changing \: limits \\ \: \\ upper \: limit \: \implies \: tan \pi = t \implies \: t = 0 \\ \\ lower \: limit \implies \: tan0 = t \implies \: t = 0 \\ \\ now \\ \\ \implies \: \int\limits_{0}^{0} \frac{1}{1 + 2t} dt \\ \\ \implies \: 0$