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  • Statement - I :    The value of the integral <img alt="\int_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}" src="https://learn.careers360.com/latex-image/?%5Cint_%7B%5Cpi%20

Statement - I :    The value of the integral \int_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}      is equal  to  \frac{\pi }{6}

Statement - II :      \int_{a}^{b}f(x)dx=\int_{a}^{b}f(a+b-x)dx

 

Option: 1

Statement - I is false; Statement - II is true

 


Option: 2

Statement - I is true ; Statement - II is true; Statement - II is a correct explanation for Statement-I

 


Option: 3

Statement - I is true ; Statement - II is true; Statement - II is not a correct explanation for Statement-I

 


Option: 4

Statement - I is true; Statement - II is false

 


Answers (1)

best_answer

I=\int_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{dx}{1+\sqrt{\tan x}}\\

I=\int_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{dx}{1+\sqrt{\cot x}}

2I=\int_{\frac{\pi }{6}}^{\frac{\pi }{3}}dx=\frac{\pi }{6}\\ I=\frac{\pi }{12}

Hence statement I is false and statement II is true 

Posted by

Rakesh

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