InterviewSolution
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InterviewSolution
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Evaluate `int_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))` |
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Answer» `I= int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tan x))` `= int_(pi/6)^(pi/3) dx/(1 + sqrt(sinx/cosx))` `I= int _(pi/6)^(pi/3) (sqrt(cosx))/(sqrtcosx + sqrtsinx) dx` `int_a^b f(x) = int_a^b f(a+b-x) dx` `I= int_(pi/6) ^ (pi/3) ( sqrt (cos(pi/3 + pi/6 -x))/(sqrt(cos(pi/3 + pi/6 - x)) + sqrt(sin(pi/3 + pi/6 - x))))dx` `I = int _(pi/6) ^(pi/3) (sqrt sinx)/(sqrt sinx + sqrt cosx ) dx` `2I= int_(pi/6)^(pi/3) ( sqrt cosx + sqrt sinx)/(sqrt sinx + sqrt cosx) dx` `2I= int _(pi/6)^(pi/3) 1.dx` `2I= pi/3 - pi/6= pi/6` `I= pi/12` Answer |
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