InterviewSolution
Saved Bookmarks
| 1. |
`int[sqrt(cotx)+sqrt(tan x)]dx` ज्ञात कीजिए!A. `sqrt2tan^(-1)((tanx)/(sqrt(2 tan x)))+C`B. `sqrt2tan^(-1)((tanx-1)/(sqrt(2 tan x)))+C`C. `(tanx)/(sqrt2)*tan^(-1)((cot x+1)/(sqrt(2 tanx)))+C`D. `(tanx)/(sqrt2)*tan^(-1)((cotx+1)/(sqrt(tanx)))+C` |
|
Answer» Correct Answer - B Let `I=int((sin x+cosx))/(sqrtsinx*cos x)dx` `=int(sqrt2(sinx+cos x))/(sqrt(2sin x*cos x))dx` `=sqrt2 int(sin x+cos x)/(sqrtsin 2x)dx` Put `sinx -cos x=t` `implies(cos x+sin x)dx=dt` Also, `sin 2x=(1-t^(2))` `thereforeI=sqrt2int(dt)/(sqrt(1-t^(2)))` `=sqrt2sin ^(-1)t+c` `=sqrt2sin ^(-1)(sinx-cos x)+c` `=sqrt2 tan ^(-1)((tan x-1)/(sqrt(2 tan x)))+c` |
|