InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`intsqrt((1-sqrt(x))/(1+sqrt(x)))` का मान ज्ञात कीजिए। |
|
Answer» माना `sqrt(x) = cos 2 theta` `rArr (1)/(2sqrt(x)) dx = -2sin 2theta d theta ` `rArr" "dx = - 2sqrt(x).2sin 2 theta d theta = - 4cos2 theta sin 2theta d theta` `thereforeint sqrt((1-sqrt(x))/(1+sqrt(x))) dx` `= int sqrt((1-cos2theta)/(1+cos 2 theta)).(-4 cos 2 theta sin 2 theta )d theta` `= int (sin theta)/(cos theta) (- 4 cos 2 theta . 2 sin theta cos theta) d theta` `= - 8 int cos 2theta sin ^(2) theta d theta` `8 int cos 2 theta.((1-cos 2theta))/(2) d theta` `= - 4((sin 2theta)/(2) - int (1+cos 4theta)/(2) d theta)+c` ` = - 2(sin 2 theta - 2theta - (sin 4 theta)/(4))+c` `=-2 sin 2 theta + 2theta +(1)/(2) . 2 sin 2 theta cos 2 theta + c` ` = - 2 sqrt(1-x)+cos^(-1)sqrt(x)+sqrt(1-x). sqrt(x+c)` |
|