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ggrree Group TitleBest ResponseYou've already chosen the best response.0
I was able to separate the integrand into partial fractions but then I get stuck.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Is that a typeo?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[\int\limits_{0}^{9}\frac{dx}{x^26+5}\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Is it really suppose to be x^26+5 and not x^26x+5?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[\frac{1}{x^21} \text{ since } 6+5=1\] \[\frac{1}{(x1)(x+1)}=\frac{A}{x1}+\frac{B}{x+1}\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[\frac{1}{(x1)(x+1)}=\frac{A(x+1)+B(x1)}{(x1)(x+1)}\] => 1=x(A+B)+(AB) A+B=0 ; AB=1
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Can you do the test now?
 2 years ago

myininaya Group TitleBest ResponseYou'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]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
You will have to break up the integral
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[\int\limits_{0}^{1}\frac{dx}{x^21} +\int\limits_{1}^{9}\frac{dx}{x^21}\]
 2 years ago

myininaya Group TitleBest ResponseYou'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
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
lol I meant rest above not test
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
@ggrree any questions?
 2 years ago

apoorvk Group TitleBest ResponseYou'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: \[\int\limits(1/(x^2a^2))dx =(1/2a)\ln((xa)/(x+a)) + k\]
 2 years ago

apoorvk Group TitleBest ResponseYou've already chosen the best response.1
dw:1332635709657:dw
 2 years ago

ggrree Group TitleBest ResponseYou've already chosen the best response.0
Yeah, I think I got it. I think... I think it diverges. is that right?
 2 years ago

ggrree Group TitleBest ResponseYou've already chosen the best response.0
thanks guys!
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
you are right! @ggrree does not converge :)
 2 years ago
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