InterviewSolution
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InterviewSolution
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Statement - I : The value of the integral `int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx))`is equal to `pi/6`.Statement - II : `int_a^bf(x)dx=int_a^bf(a+b-x)dxdot`(1)Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I(2)Statement -I is True; Statement -II is False.(3)Statement -I is False; Statement -II is True(4)Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I |
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Answer» `i = int_(pi/6)^(pi/3) dx/(1 + sqrt tan x) ` `= int_(pi/6)^(pi/3) dx/(1 + sqrt(tan(pi/3 + pi/6 - x))` `= int_(pi/6)^(pi/3) dx/(1 + sqrt cot x) ` `= int_(pi/6)^(pi/3) (sqrt tan x)/(sqrt tan x + 1) dx` equation `1+ 2` `2i = int_(pi/6)^(pi/3) (1 + sqrt tan x)/(1 + sqrt tan x) dx` `2i = x` `2i = pi/3 - pi/6` `2i = pi/6` `i=pi/12` option 3 is correct |
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