## quakeash 3 years ago what is the integral of 2/ (2x-x^2)^1/2 my guesses is sin^-1 (whatever) +c maybe ?

1. experimentX

??

2. experimentX

integral of ??

3. quakeash

the integral of x/ (2x-x^2)^1/2

4. experimentX

try completing squares .. 2x - x^2 = 1 - (1-x)^2

5. experimentX

and let 1 - x = sin u, x = 1 + sin u

6. experimentX

not sure though ... haven't checked!!

7. quakeash

the complete square u gave me is wrong its 1-(x-1)^2 i guess right ?

8. shivam_bhalla

@quakeash , would you mind writing your question on drawing board again? Click the draw button below and rewrite your question on that

9. shivam_bhalla

|dw:1337271739470:dw| Is this your question ??

10. quakeash

exactly

11. experimentX

LOL ... it wasn't trig substitution, http://www.wolframalpha.com/input/?i=integrate+x%2F%28sqrt%282x+-+x^2%29%29

12. shivam_bhalla

It is pretty simple. First follow what @experimentX said |dw:1337271981227:dw|

13. shivam_bhalla

|dw:1337272062537:dw|

14. shivam_bhalla

soory mistake in the lat step

15. shivam_bhalla

It should be |dw:1337272154314:dw|

16. quakeash

the solution . since the integral of dx/(a^2 - x^2) = sin^-1 (x/a) + c then my question after completing square would be .. 2/(1-(x-1)^2)^1/2 and its sin ^-1 (x-1/1) +c /////////////// case closed :D

17. shivam_bhalla

Now substitute back x -1 in place of t . You will get your answer