Integral Calculus Question 305
Question: $ \int_{{}}^{{}}{{{{1+2\tan x(\tan x+\sec x)}}^{1/2}}dx=} $
[Roorkee 1987]
Options:
A) $ \log (\sec x+\tan x)+c $
B) $ \log {{(\sec x+\tan x)}^{1/2}}+c $
C) $ \log \sec x(\sec x+\tan x)+c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{{{(1+2{{\tan }^{2}}x+2\tan x\sec x)}^{1/2}}dx} $ $ =\int_{{}}^{{}}{{{({{\sec }^{2}}x+{{\tan }^{2}}x+2\tan x\sec x)}^{1/2}}dx} $ $ =\int_{{}}^{{}}{(\sec x+\tan x),dx}=\log (\sec x+\tan x)+\log \sec x+c $ $ =\log \sec x(\sec x+\tan x)+c $ .
BETA
