psk981
Evaluate: Please look at the integral
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psk981
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\[\int\limits_{C}^{} F.T ds \] for a vector field F=x ^{2}i-yj
psk981
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from (2,4) to (1.1)
psk981
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|dw:1352896610110:dw|
experimentX
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along the straight line? what is T ?
psk981
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you have to find flow
experimentX
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|dw:1352897206497:dw|
psk981
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how did u get r(t) i know you used the points but why did u pick t for the second set of points
amistre64
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the t used is just a variable scalar to stretch the vector to all point along the line from the point used to anchor it to the line
psk981
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so how would i find F. dr/dt where T=dr/dt?
amistre64
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i dont recall the flow stuff to clearly, but does this look familiar?
\[\frac{dr}{dt}=\frac{dr}{dx}\frac{dx}{dt}+\frac{dr}{dy}\frac{dy}{dt}\]
psk981
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looks like chain rule
amistre64
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this is a line integral right?
psk981
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r(t)= <2-t, 4-3t>
psk981
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F=(2-t)^2i-(4-3t)j
amistre64
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i believe we also need r'
psk981
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how would i get it i know its a derivative would it be r(t)= -i-3j
psk981
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r'(t)=-i-3j
amistre64
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then thats its; dot F and r' together to get a scalar equation to integrate
right?
psk981
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yes its F. dr/dt
psk981
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i am not sure abt the dr/dt part
amistre64
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r= <2-t, 4-3t>
r'= <(2-t)', (4-3t)'>
r'= <-1, -3>
amistre64
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F=<(2-t)^2 ,-4+3t>
dot r'=< -1 , -3 >
-----------------------
-(2-t^2)+12-9t
amistre64
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got me ^2 in the wrong side ... :/
amistre64
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the line is from t=0 to t=1 giving us\[\int_{0}^{1}-4-t^2+4t-9t+12~dt\]\[\int_{0}^{1}-t^2-5t+8~dt\]
amistre64
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do you have an answer key to check with by chance?
psk981
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nope
amistre64
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well, weve followed the simple directions from pauls site; so it should be good ;)
psk981
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these vector fields so confusing
amistre64
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indeed they are
psk981
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i have another vector question
amistre64
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the Force equation gives us the force at each for each x,y point along the line
the lines vector equation gives us the x and y values along the path
F(r) is just defining the forces along the path; dotting with r' tho has me a little baffled at an explanation at the moment tho ;)
psk981
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how do i draw a vector field
amistre64
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for each lattice point on a graph you draw a little arrow indicating the direction and magnitude of the vector associated with the values of x and y (or whatever reference frame your using) at that point