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Calculus III: Fundamental Theorem of Line Integrals problem

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Pupil
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Date Posted: 5/12/2008 11:13:59 PM  Status: Closed
Calculus III: Fundamental Theorem of Line Integrals problem
Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:
the question is F = ysin(xy)i + xsin(xy)j and C is the parabola y = 2x2 from (1,2) to (3,18). How do you do this problem?
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Sage
Karma Points: 5,570
Date Posted: 5/12/2008 11:26:59 PM  Status: Live
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Response:



So if you can find a function such that [meaning your field is conservative]


Then your line integral is independent of path and you can just evaluate at the endpoints

In particular, you're looking for a function f such that


by definition of gradient we know are field is of the form.

Therefore it follows that


If we integrate this with respect to x we get f(x,y) + a constant that is a function of y (since we treat y as a constant)


If we take the derivative of this with respect to y, we get fy


but we know that fy is xsin(xy).  setting the two equal



or some constant, which when we evaluate will disappear


Therefore
semaj's Comment:
and here I was thinking you can't take the anti-derivative of them. thanks man

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Oracle
Karma Points: 14,052
Date Posted: 5/12/2008 11:34:01 PM  Status: Live
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semaj's Comment:
already been helped, but heres a rating =P
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I have a strong resistance to understanding the relationship between voltage and current. :)



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