A) 0
B) 1
C) does not exist
D) None of these
Correct Answer: C
Solution :
\[\int_{0}^{\pi /4}{\frac{\sec x\cos ecx}{\log (\tan x)}}dx\] \[=\int_{0}^{\pi /4}{\frac{\sec x}{\sin x\log (\tan x)}}dx\times \frac{\sec x}{\sec x}\] \[=\int_{0}^{\pi /4}{\frac{{{\sec }^{2}}x}{\tan x\log (\tan x)}}dx\] Put log tan \[x=z\] \[\Rightarrow \] \[\frac{1}{\tan x}.{{\sec }^{2}}xdx=dz\] When \[x=0,\text{ }z=\infty \] \[x=\pi /4,\text{ }z=0\] \[\therefore \] \[\int_{\infty }^{0}{\frac{1}{z}}dx=[\log z]_{\infty }^{0}\] = does not exist
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