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A particle travels on an elliptic course x^2/4+y^2=1 (x,y>=0) from point A(0,1) to point B(2,0)

On it works the following force:

F=(1+xy)e^(xy) i + x^2e^(xy) j

Calculate work of the force .

Now I have this law:

W = Integral(AB) (1+xy)e^(xy) dx + x^2 e^(xy) dy (see figure. beneath)

I have calculated the Integral as this:

w=1/y * e^(xy) + x*e^(xy)-e^(xy)+x*e^(xy)

the problem is when I insert y=0 I have division by zero ,so what am I doing wrong? how to go about this?

(I'm new to the subject!)

On it works the following force:

F=(1+xy)e^(xy) i + x^2e^(xy) j

Calculate work of the force .

Now I have this law:

W = Integral(AB) (1+xy)e^(xy) dx + x^2 e^(xy) dy (see figure. beneath)

I have calculated the Integral as this:

w=1/y * e^(xy) + x*e^(xy)-e^(xy)+x*e^(xy)

the problem is when I insert y=0 I have division by zero ,so what am I doing wrong? how to go about this?

(I'm new to the subject!)

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https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic

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Start your 7-day free trialYou see when I parametrized my integral and curve I still got an unsolvable Integral!

for example what is the Integral of: e^(cost*sint) ?

I will upload it soon.

Thank you all for your help.

One of the videos demonstrated that changing the direction of a vector line integral just changes the sign. So, you can just keep track of signs and still use Green's theorem if you want.

I did not check the details of your last post, but did come up with the same answer by observing that pdQ/pdx = pdP/pdy and therefore the force field is conservative. Then, choose the path A -> O and O -> B to avoid the elliptical (harder to integrate) path.

A -> O gives work = 0.

O -> B gives work = 2.

Math / Science

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remember that e^0 = 1

calculate the work done by the x component separately then the work done by the y component.