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Integration Problem

by lost_2
Tags: integration
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lost_2
#1
Apr14-08, 10:20 AM
P: 5
HI there!! i was wondering if you could help me with this..

how do you integrate -2xy/(1+x^2)?

Thank you.
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Hootenanny
#2
Apr14-08, 10:23 AM
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Quote Quote by lost_2 View Post
HI there!! i was wondering if you could help me with this..

how do you integrate -2xy/(1+x^2)?

Thank you.
Welcome to the forums,

Your question is incomplete. What are you integrating with respect to? Is y a function of x or vice versa?

As an aside, feel free to post a new topic for each new question, you don't need to tag your question on the end of others/
lost_2
#3
Apr14-08, 10:28 AM
P: 5
Hey!

Thanks for the quick reply.. Coz it a similar qns so i posted together with this. That equation is the gradient of a curve. So it's just to integrate with respect to x? How do you go about doing it?

Thank you.

lost_2
#4
Apr14-08, 11:09 AM
P: 5
Integration Problem

Anyways this is the whole qns.

find the equation of the curve in the xy plane that passes through (1,2) and whose tangent line at a point (x,y) has a slope of -2xy/(1+x^2).
Hootenanny
#5
Apr14-08, 12:27 PM
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Quote Quote by lost_2 View Post
Anyways this is the whole qns.

find the equation of the curve in the xy plane that passes through (1,2) and whose tangent line at a point (x,y) has a slope of -2xy/(1+x^2).
Thanks, it's always a good idea to post the entire question. So you know that,

[tex]\frac{dy}{dx} = -\frac{2xy}{1+x^2}[/tex]

Which is a first order ODE. What methods do you know for solving first order ODE's?
lost_2
#6
Apr14-08, 08:22 PM
P: 5
by using variable separable method?
lost_2
#7
Apr14-08, 08:41 PM
P: 5
is the answer y(1+x^2)= c?
HallsofIvy
#8
Apr15-08, 05:16 AM
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Thanks
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You have not yet used the fact that the curve passes through (1, 2).


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