InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`int (dx)/(sin(x-a)sin(x-b)`A. `sin(b-a)log|(sin(x-b))/(sin(x-a))|+C`B. `cosec(b-a)log|(sin(x-a))/(sin(x-b))|+C`C. `cosec(b-a)log|(sin(x-b))/(sin(x-a))|+C`D. `sin(b-a)log|(sin(x-a))/(sin(x-b))|+C` |
|
Answer» Correct Answer - A `I = int(dx)/(sin(x-a)sin(x-b))` `= (1)/(sin(b-a))int(sin(b-a))/(sin(x-a)sin(x-b))dx` `= (1)/(sin(b-a))int(sin(x-a-x+b))/(sin(x-a)sin(x-b))dx` `= (1)/(sin(b-a))int(sin{(x-a)-(x-b)})/(sin(x-a)sin(x-b))dx` `= (1)/(sin(b-a)) int(sin(x-a)cos(x-b)-cos(x-a)sin(x-b))/(sin(x-a)sin(x-b))dx` `= (1)/(sin(b-a)) int[cot(x-b)-cot(x-a)]dx` `= (1)/(sin(b-a)) [log|sin(x-b)|-log|sin(x-a)|]+C` `= cosec (b-a)log|(sin(x-b))/(sin(x-a))|+C` |
|