Question

calculus 2 - partial fractions

Answer 1

\[\frac{a}{4-x}+\frac{b}{4+x}\] solve for \(a,b\)

Answer 2

you can ignore the 40 if you like and pull it out of the integral or leave it in
there is a real quick snappy way to do this
do you know it?

Answer 3

wanna do it with the 40 or without?

Answer 4

no i don't. Whichever is the best and quickest way in your opinion

Answer 5

lets leave it in
start with
\[\frac{40}{(4-x)(4+x)}=\frac{A}{4-x}+\frac{B}{4+x}\] then \(4-x\) is 0 if \(x=4\) so put your finger over the factor of \(4-x\) in the original expression and replace \(x\) by \(4\)
\[\frac{40}{\cancel{(4-x})(4+4)}=\frac{40}{8}=5\] and so \(A=5\)

Answer 6

shouldn't that not work since you are placing 4 in x for both sides?

Answer 7

A/ (4-4) is undefined?

Answer 8

that is why you cover it up with your finger when you compute

Answer 9

i was only plugging 4 in on the left

Answer 10

is that legal in math?

Answer 11

\[A=\frac{40}{\cancel{(4-x})(4+4)}=\frac{40}{8}=5\]

Answer 12

it is just a quick technique
you accomplish the same thing by writing
\[40=A(4+x)+B(4-x)\] and then saying "let \(x=4\)"

Answer 13

Ok, I get it. You have to times (4-x) on each side first to cancel them out.

Answer 14

you would get
\[40=8A\] and so \(A=5\) same idea exactly

Answer 15

just a quick gimmick is all, but it works nicely
btw i thing \(B=5\) as well

Answer 16

*think

Answer 17

ok cool. what to do from there?

Answer 18

\[\int \frac{5}{4-x}dx+\int \frac{5}{4+x}dx\] should be immediate right?

Answer 19

i think so

Answer 20

i am wondering if i made a mistake somewhere

Answer 21

no, i am sticking with my answer

Answer 22

What would the final answer be?

Answer 23

well my problem is that wolfram gave me a different answer, but i like my answer of
\[5\ln(4-x)+5\ln(4+x)\]

Answer 24

i tried the 3rd and fifth bubble. both are wrong

Answer 25

i get 3, but wolfram gets 4

Answer 26

on the other hand, if you take the derivative of number 3 you get \(\frac{40}{16-x^2}\) so i am not sure what is wrong

Answer 27

should i try the 4th bubble? This is my last guess

Answer 28

http://www.wolframalpha.com/input/?i=40%2F%2816-x^2%29

Answer 29

wolf get
\[5\ln(\frac{4+x}{4-x})\]

Answer 30

That got me the right answer

Answer 31

i still like my answer
take the derivative and it works

Answer 32

thank you

Answer 33

yw