InterviewSolution
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InterviewSolution
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`int(sqrt(tanx)+sqrt(cotx))dx` is equal toA. `sqrt2 tan^(-1)((tanx)/(sqrt(2tanx)))+C`B. `sqrt2 tan^(-1)((tanx-1)/(sqrt(2tanx)))+C`C. `(tanx)/(sqrt2).tan^(-1)((cotx+1)/(sqrt(2tanx)))+C`D. `(tanx)/(sqrt2).tan^(-1)((cotx+1)/(sqrt(2tanx)))+C` |
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Answer» Correct Answer - B Let `l=int((sin x+cosx))/(sqrt(sinx.cosx))dx` `=int(sqrt2(sinx+cosx))/(sqrt(2sinx.cosx))dx=sqrt2 int(sinx+cosx)/(sqrt(sin2x))dx` `"Put "sinx-cosx=t` `rArr" "(cosx+sinx)dx=dt` `"Also, "sin 2x=(1-t^(2))` `therefore" "l=sqrt2 int(dt)/(sqrt(1-t^(2)))=sqrt2 sin^(-1)t+C` `=sqrt2 sin^(-1)(sinx - cosx)+C` `=sqrt2 sin^(-1)(sinx-cosx)+C` `=sqrt2 tan^(-1)((tanx-1)/(sqrt(2tanx)))+C` |
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