Share
This Question is Closed
ggrree
Best Response
You've already chosen the best response.
0
I was able to separate the integrand into partial fractions but then I get stuck.
myininaya
Best Response
You've already chosen the best response.
2
Is that a type-o?
myininaya
Best Response
You've already chosen the best response.
2
\[\int\limits_{0}^{9}\frac{dx}{x^2-6+5}\]
myininaya
Best Response
You've already chosen the best response.
2
Is it really suppose to be x^2-6+5 and not x^2-6x+5?
myininaya
Best Response
You've already chosen the best response.
2
\[\frac{1}{x^2-1} \text{ since } -6+5=-1\]
\[\frac{1}{(x-1)(x+1)}=\frac{A}{x-1}+\frac{B}{x+1}\]
myininaya
Best Response
You've already chosen the best response.
2
\[\frac{1}{(x-1)(x+1)}=\frac{A(x+1)+B(x-1)}{(x-1)(x+1)}\]
=>
1=x(A+B)+(A-B)
A+B=0 ; A-B=1
myininaya
Best Response
You've already chosen the best response.
2
Can you do the test now?
myininaya
Best Response
You've already chosen the best response.
2
And by the way this is an improper integral meaning the function is not continuous on [0,9]
myininaya
Best Response
You've already chosen the best response.
2
You will have to break up the integral
myininaya
Best Response
You've already chosen the best response.
2
\[\int\limits_{0}^{1}\frac{dx}{x^2-1} +\int\limits_{1}^{9}\frac{dx}{x^2-1}\]
myininaya
Best Response
You've already chosen the best response.
2
See if both parts converge if so then take the sum in you are done
if not then the area/net area is divergent
myininaya
Best Response
You've already chosen the best response.
2
lol I meant rest above not test
myininaya
Best Response
You've already chosen the best response.
2
@ggrree any questions?
apoorvk
Best Response
You've already chosen the best response.
1
i think we have a standard formula as well for integrals of this type rather than use partial fractions every time:
\[\int\limits(1/(x^2-a^2))dx =(1/2a)\ln((x-a)/(x+a)) + k\]
apoorvk
Best Response
You've already chosen the best response.
1
|dw:1332635709657:dw|
apoorvk
Best Response
You've already chosen the best response.
1
@ggrree
ggrree
Best Response
You've already chosen the best response.
0
Yeah, I think I got it. I think... I think it diverges. is that right?
ggrree
Best Response
You've already chosen the best response.
0
thanks guys!
myininaya
Best Response
You've already chosen the best response.
2
you are right! @ggrree
does not converge :)