Saved Bookmarks
| 1. |
Evaluate : int_(0)^(1) (sin^(-1) sx)/(sqrt(1-x^(2)))dx |
|
Answer» Solution :`"LET sin"^(-1) x=t` `rArr ""(1)/(SQRT(1-x^(2)))dx =DT` `At x=0, ""t=sin^(-1) 0=0` `At x=1 ""t=sin^(-1) 1=PI//2` `:. int_(0)^(1) (sin^(-1)x)/(sqrt(1-x^(2))) dx =int_(0)^(pi//2) t dt = [(t^(2))/(2)]_(0)^(pi//2)` `=1/2 ((pi)/(2))^(2) -0=(pi^(2))/(8).` |
|