sat_chen 2 years ago did i get this partial integration question right?

1. sat_chen

|dw:1359940501331:dw|

2. sat_chen

3. sat_chen

can someone just check if that is the right answer

4. sat_chen

im still kind of confused about it

5. UnkleRhaukus

i think you've made a mistake somewhere,

6. sat_chen

ok i did it wrong apparently but i dont know how to do it still :( ?

7. hartnn

so, denominator = x^2 (x-4) do you know partial fractions method ? also, if you show your work, we can quickly spot the error, and continue from that step...

8. sat_chen

ok i will type it out for you

9. sat_chen

so first what i did was split the denominator to x(x^2-4) then split that to (x+2)(x-2)

10. sat_chen

then set the 2x^2 -12x+4=A/x+B/(x+2)+C/(x-2)

11. hartnn

here.... x^3-4x^2 = x^2 (x-4) and not x (x^2-4)

12. sat_chen

wow i cant believe i missed that

13. hartnn

since you know partial fractions , i think you'll get it in your next try..

14. sat_chen

sorry guys my intentet is acting weird

15. sat_chen

yea ill try the steps again and after im done pm you the steps

16. sat_chen

to see if i did it right thanks

17. hartnn

ok, sure. or you can post it here.. welcome ^_^

18. sat_chen

so would the partial thing be Ax+ B /x^2 +C/(x-4)

19. hartnn

yes.

20. sat_chen

and really sorrmy internet is going berserk for some reason today college inter is acting funky for some reason

21. hartnn

A/x+ B /x^2 +C/(x-4)

22. sat_chen

wait isnt when the denominator is x^2 the top part is (Ax + B )/(x^2)

23. hartnn

its the same thing! (Ax+B)/x^2 = A/x + B/x^2

24. sat_chen

yep really had a long day today -.- after the superbowl drink and math dont go together

25. hartnn

lol.

26. sat_chen

ok after im done ill post the answer ty

27. sat_chen

so 2x^2-12x+4 = A/x + B/x^2 +c/(x-4)

28. sat_chen

and i solved for c which got me -3/16

29. sat_chen

|dw:1359956605483:dw|

30. sat_chen

and i plugged in as x = 4;

31. sat_chen

to get c = -3/16 but you cant solve for the other A and B is there another method to do this? i dont get partial fractions

32. hartnn

to find c, put x=4 to find b, put x=0 to find a, put x=any other value, say x=1

33. hartnn

what part of partial fractions, do you not get ?

34. sat_chen

if you put x = 0 you will get all 3 = 0

35. hartnn

u sure ?

36. sat_chen

|dw:1359957041709:dw| so you cant put 0

37. sat_chen

yea i got the c one though with is at x = 4

38. hartnn

......+B (x-4)+.....

39. hartnn

A x (x-4) +B (x-4) +C (x^2)

40. sat_chen

|dw:1359957163440:dw|

41. sat_chen

wait can you tell me how you got that i got the trigonometric integral stuff but this stuff is confusing me

42. sat_chen

so can you tell me how you cancelled out the x in the B and the x in the A

43. hartnn

|dw:1359957466093:dw|

44. hartnn

|dw:1359957564998:dw|

45. sat_chen

shouldnt A/x be multiplied by |dw:1359957703525:dw|

46. hartnn

then denominator of A will become x^3 (x-4) which we don't want and is not common

47. sat_chen

hold on what i meant was isnt the format |dw:1359957835056:dw|

48. sat_chen

|dw:1359958002008:dw| i guess what i mean is in this for example why did you only pick out x(x-4) for A only (x-4) for b and x^2 for C im really confused about that

49. hartnn

so, that i have SAME denominator for all the 3.

50. sat_chen

and also because in previous problems i did it was like 4x^2 + 54 x + 134 = A/(x-1) +B/(x+5) +C/(x+3) which i got to 4x^2 + 54x + 134 = A(x+5)(x+3) + B(x-1)(x+3)+C(x-1)(x+5)

51. sat_chen

do you have to do this when the denominator has a square on the x? or is it dependent on the problem

52. hartnn

|dw:1359958265843:dw|its as simple as this...

53. hartnn

do what ?

54. sat_chen

oh i see i guess you could multiply what i did but it would cancel

55. sat_chen

i think i finally get it now

56. hartnn

in previous problem, to make the common denominator as (x-5)(x+5)(x+3) so, you multiplied and divided by (x+5)(x+3) for A yes, you can say that also...

57. sat_chen

now if i had payed attention in my algebra classes this would be so much easier -.-

58. hartnn

no problem! because its easier for you now! right ?