InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Evaluate:`int(dx)/((a^2+x^2)^(3/2))` |
|
Answer» Put `x=a tan theta implies dx = a sec^(2) theta d theta` ` :. I= int (dx)/(a^(2)+x^(2))^(3//2)` `= int(a sec^(2)theta)/((a^(2)+a^(2) tan^(2)theta)^(3//2))d theta` `=int(a sec^(2)theta)/(a^(3)(sec^(2)theta)^(3//2))d theta` `=(1)/(a^(2))int(d theta)/(sec theta)` `=(1)/(a^(2))int cos theta d theta` `=(1)/(a^(2))sin theta +c` Now `tan theta=(x)/(a)` ` :. sin theta = (x)/(sqrt(x^(2)+a^(2)))` ` :. I= (x)/(a^(2)sqrt(x^(2)+a^(2)))+c` |
|