In my emag course we are reviewing vector calculus. I've forgotton a lot over the summer, so I just want to make sure I'm doing this properly.(adsbygoogle = window.adsbygoogle || []).push({});

question)

[tex] \vec E = \hat x y + \hat y x [/tex]

Evaluate [itex] \int \vec E \cdot d\vec l [/itex] from [itex] P_1(2,1,-1) [/itex] to [itex] P_2(8,2,-1) [/itex] along the parabola [itex] x = 2y^2 [/itex].

sol)

We are in cartesian coordinates, thus:

[tex] d\vec l = \hat x dx + \hat y dy [/tex]

[tex] \vec E \cdot d\vec l = ydx + xdy [/tex]

Our path is:

[tex] x=2y^2 [/tex]

[tex] y=\sqrt{\frac{x}{2}}[/tex]

Thus,

[tex] \int_2^8 \sqrt{\frac{x}{2}}\,\,dx + \int_1^2 2y^2 \,\,dy = \frac{28}{3}+\frac{14}{3}=14 [/tex]

Does everything look ok?

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# Homework Help: Really simple line integral

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