Finding the value of a line integral: (xcos(z)-yze^x)i+(xcos(z)-ze^x)j-(xysin(z)+ye^x

mathpro18

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Dec 13, 2015
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I am to find the line integral of (xcos(z)-yze^x)i+(xcos(z)-ze^x)j-(xysin(z)+ye^x)k where c is given by the following parametric description:

x=4cos(2t)
y=2sin(2t)

I'm not sure how do to this because the vector field is three dimensional while the region is two dimentional so I can't find f*dr. Unless I can assume z=0. I tried to see if this was a conservative vector field and it was not(curl(f)≠0). I'm also unsure what my bounds on the integral would be(What t varies between).
 
I am to find the line integral of (xcos(z)-yze^x)i+(xcos(z)-ze^x)j-(xysin(z)+ye^x)k where c is given by the following parametric description:

x=4cos(2t)
y=2sin(2t)


I'm not sure how do to this because the vector field is three dimensional while the region is two dimentional so I can't find f*dr. Unless I can assume z=0. I tried to see if this was a conservative vector field and it was not(curl(f)≠0). I'm also unsure what my bounds on the integral would be(What t varies between).

That is an equation of a closed curve (e.g. ellipse → x2 + 4y2 = 22)
 
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