## anonymous 5 years ago Can someone explain me the steps of solving integrals using partial fractions?

1. anonymous

Should i give you am example?

2. anonymous

the integration is usually the easy part. finding the decomposition is a pain often

3. anonymous

ya i don't get the steps. my book didnt tell me

4. anonymous

|dw:1326817894193:dw|

5. anonymous

$\frac{1}{(x-2)(x-3)}=\frac{a}{x-2}+\frac{b}{x-3}$ and you need a and b. we know that $a(x-3)+b(x-2)=1$ so this is an easy one. since this equality has to be true for all values of x, it must be true if x = 2, so you get $a(2-3)+b(2-2)=1$ $-a=1$ $a=-1$

6. anonymous

lol they got a diff answer is that ok?

7. anonymous

How about using heavy side cover up for this one?

8. anonymous

repeat the process making x = 3, and you will find $b=1$ so we have $\frac{1}{(x-2)(x-3)}=\frac{-1}{x-2}+\frac{1}{x-3}$ and now integrate term by term. now it is not ok

9. anonymous

*no

10. anonymous

They got 1/3 and -1/3

11. anonymous

then maybe i made a mistake, let me write it out

12. TuringTest

is that a 5 on the second set of parentheses?

13. TuringTest

sat used a 3

14. anonymous

doh, i used 3!!

15. anonymous

LOL ya sorry abt that

16. anonymous

ohhh didnt even notce that sat

17. TuringTest

sat has done it correctly for sure, just with the wrong number

18. anonymous

no that is my fault, but idea is clear right?

19. anonymous

$a(x-5)+b(x-2)=1$ let $x=2$ get $-3a=1,x=-\frac{1}{3}$

20. anonymous

ummmm so y did u chose the value 2?

21. anonymous

i am going to wager you can figure out why i picked 2

22. anonymous

and what i will pick next also

23. anonymous

need a hint?

24. anonymous

well cuz it is in the denomanator? lol

25. anonymous

i have this equality $a(x-5)+b(x-2)=1$ and i am looking for a and b. so how can i find a easily?

26. anonymous

by eliminating one variable by making one part =0

27. anonymous

K i got that LOL

28. anonymous

zactly. so first we let x =2, and then we let x = 5

29. anonymous

oh ok got that :D Thanks :D

30. anonymous

yw

31. anonymous

I thought u guys started teaching today

32. anonymous

This one a is a simple one if I have a more difficult one I will be back :D

33. anonymous

with some practice you can do this: write $\frac{1}{(x-2)(x-5)}=\frac{a}{x-2}+\frac{b}{x-5}$ now to find a, put your finger over the x - 2 in the first expression, put x = 2 and get $a=\frac{1}{2-3}=-\frac{1}{3}$

34. myininaya

its called office hours

35. anonymous

Thanks sat :D

36. anonymous

i really need to get back to work, but i have 30 emails to send out and got bored bored bored. later

37. anonymous

LOL bye