## aayushi.somani 8 months ago Integrate : (x-1) root(1-x-x^2)

1. myininaya

Have you tried completing the square inside the square root first?

2. myininaya

This might end up being a trig sub.

3. myininaya

i will be back if you have questions

4. aayushi.somani

yeah i tried it.. but that didnt worked !

5. vaibhavthacker95

u can take (x-1) as u and the rest term as v and integrate by parts

6. aayushi.somani

7. ikram002p

addy :o is it like this ? $$\int (x-1) \sqrt (1-x-x^2)$$

8. aayushi.somani

yeah exactly!

9. myininaya

The trig sub seems to work Not saying there aren't other ways though

10. myininaya

@aayushi.somani may I ask how far you got with that method?

11. myininaya

to what integral have you transformed it?

12. aayushi.somani

i could not figure out anything

13. myininaya

can you tell me what substitutions you performed ?

14. myininaya

some people like to do two here i just like one

15. myininaya

When you say you could not figure out anything does that mean you did not do anything with the trig sub even though you said you did?

16. myininaya

I'm confused

17. aayushi.somani

i tried getting a trig sub but unfortunatly i couldnt.. thats what it is.. @ikram002p could u figure out?

18. myininaya

did you complete the square inside the square root part?

19. aayushi.somani

if i could have done it then y would i ask this ques..??? @myininaya i asked so that anyone could help me..

20. myininaya

Oh I'm sorry I didn't know you couldn't do the algebra either

21. myininaya

So by nothing means absolutely nothing I get it

22. aayushi.somani

from what i did m getting a wrong answer so consider i did nothing and now please help me from the very begnning..

23. myininaya

$ax^2+bx+c=a(x^2+\frac{b}{a}x)+c=a(x^2+\frac{b}{a}x+(\frac{b}{a})^2)+c-a(\frac{b}{a})^2 \\ =a(x+\frac{b}{a})^2+c-a \frac{b^2}{a^2}=a(x+\frac{b}{a})^2+c-\frac{b^2}{a}$ I hope this helps you complete the square Please follow these steps I prefer you ask me questions on how to do this than just using the end result there

24. ikram002p

|dw:1408601698600:dw| i dont know if this work next to use tring mmm sin maybe ?

25. myininaya

oh mine what is all of that?

26. aayushi.somani

u mean i gotto Rationalise? @ikram002p

27. myininaya

You don't have to rationalize...And tht wouldn't be the way to rationalize the top anyhow

28. ikram002p

:P ok we dont need conjucate xD just hmm 1-x-^2=(5/2-(x+1/2)^2 >.<

29. aayushi.somani

got it lol sorry :P

30. aayushi.somani

i got the answer.. anyways thanks (:

31. ikram002p

:o how did u get it ?

32. aayushi.somani

I just made a small mistake.. I rechecked it.. and i could figure out the mistake! thankyou so much.. @ikram002p

33. ikram002p

:* np girl

34. myininaya

I thought you didn't do any of it...

35. myininaya

I want to go back to my completing square thingy... (i made some mistakes) $ax^2+bx+c=a(x^2+\frac{b}{a}x)+c=a(x^2+\frac{b}{a}x+(\frac{b}{2a})^2)+c-a(\frac{b}{2a})^2 \\ =a(x+\frac{b}{2a})^2+c-a \frac{b^2}{4a^2}=a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a}$