InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
फलन `int(dx)/(2sqrt(x(1-x)))` का x के सापेक्ष समाकलन कीजिए । |
|
Answer» माना `I=int(dx)/(2sqrt(x(1-x)))=(1)/(2)int(dx)/(sqrt(-(x^(2)-x)))` `=(1)/(2)int (dx)/(sqrt(-(x^(2)-x+(1)/(4)-(1)/(4))))" "` (पूर्ण वर्ग बनाने पर ) `I=(1)/(2)int(dx)/(sqrt(((1)/(2))^(2)-(x-(1)/(2))^(2)))` माना ` x-(1)/(2)=t therefore dx=dt` तथा `(1)/(2)=a` `therefore" "I=(1)/(2)int(dt)/(sqrt(a^(2)-t^(2)))=(1)/(2)sin^(-1)((t)/(a))` `=(1)/(2)sin^(-1)((x-(1)/(2))/((1)/(2)))=(1)/(2)sin^(-1)((2x-1)/(1))` `thereforeI=(1)/(2)sin^(-1)(2x-1)` |
|