cherrilyn
  • cherrilyn
evaluate the integral
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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cherrilyn
  • cherrilyn
\[\int\limits_{?}^{?}100xdx/(x-3)(x ^{2}+1)^{2}\] I know I change it to A/x-1 + B(x-1)^2+C(x-1)^3 then multiply it by (x-1)^3 then what
anonymous
  • anonymous
are you sure?
cherrilyn
  • cherrilyn
oops I mean A/x-3 + Bx+C/x^2+1 + Dx+E/(x^2+1)^2

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anonymous
  • anonymous
lol
anonymous
  • anonymous
alright, good , now start taking small values for x ^_^ to find A, B, C and D
anonymous
  • anonymous
wait, first you have to multiply the denominator on all parts
anonymous
  • anonymous
Take x=3. You will find A directly.
anonymous
  • anonymous
A=3
anonymous
  • anonymous
so, you'll get :\[100x = A(x+1)^2 + Bx + C(x-3)(x^2+1) + Dx + E (x-3)\]
cherrilyn
  • cherrilyn
ok A=3 :)
cherrilyn
  • cherrilyn
wait no
anonymous
  • anonymous
now you can take values for x to find all the alphabets ^_^
anonymous
  • anonymous
hmm, what?
cherrilyn
  • cherrilyn
when you distribute in..for example.. Bx+C(x-3)(x^2+1) ... do you distribute the two things in the parenthesis to the Bx AND the C? or just the C
cherrilyn
  • cherrilyn
and Distribute (x-3) to the Dx AND the E?
anonymous
  • anonymous
hmm, I think it's the whole thing
anonymous
  • anonymous
yes yes, I'm sure
cherrilyn
  • cherrilyn
okay so A is indeed 3
anonymous
  • anonymous
yes it is ^_^
anonymous
  • anonymous
The better way is to open all brackets, and add like terms together.
anonymous
  • anonymous
now take other values for x, such as -1 1 2 -2 ~
anonymous
  • anonymous
B=0
anonymous
  • anonymous
Oh wait!!
cherrilyn
  • cherrilyn
blaah do I have to test all of those numbers? lol its kiind of hard to predict the right values just by looking at it
anonymous
  • anonymous
yes it's a must, you need to get all the values, A, B,C,D,and E
cherrilyn
  • cherrilyn
I mean the numbers -1, 1, 2, and -2
anonymous
  • anonymous
yes , you must lol, what other way is there to solve it?
anonymous
  • anonymous
you must check with all values my dear :)
anonymous
  • anonymous
B=-3
anonymous
  • anonymous
C=9
anonymous
  • anonymous
you checked the values? anwar? or shall I check after you lol
anonymous
  • anonymous
D=18
cherrilyn
  • cherrilyn
Okay If I plug in A=3 and x=-1..... I get -100=12+2B-2C+4D-4E. now what? Or am I doing this wrong
anonymous
  • anonymous
no you're write, so now you have equation 1, you can use it later to either subtract or add from another equation ^_^
anonymous
  • anonymous
right*
anonymous
  • anonymous
alright I gtg, I'll be back later, bye ^_^
cherrilyn
  • cherrilyn
okay thankss! Ttyl :)
anonymous
  • anonymous
anwar will continue, most welcome :)
anonymous
  • anonymous
I got all of them. Hopefully right!
anonymous
  • anonymous
A=3, B=-3, C=9, D=24, E=-8
anonymous
  • anonymous
Bye starica!!
cherrilyn
  • cherrilyn
thanks anwar!
anonymous
  • anonymous
You're welcome!! You may want to check them.
anonymous
  • anonymous
OMG, Sorry there was a mistake.
anonymous
  • anonymous
It should be: A=3, B=-3, C=-9, D=-30, E=10. Sorry for the confusion.
cherrilyn
  • cherrilyn
what values for x did you use?
anonymous
  • anonymous
Well.. I opened all the parenthesis, and add like terms together, and then solved the equations.
anonymous
  • anonymous
For example if you have x^2(A+B)+x(C+2B)=5x^2+x, that means: A+BC=5 and C+2B=1.. I used this idea.

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