WD Line Integrals

Calculate the work done by the force field $F(x,y,z)=(y^2,z^2,x^2)$ along the curve of intersection of the sphere $x^2+y^2+z^2=1$, the cylinder $x^2+y^2=x$, and the halfspace $z>0$. The path is traversed in a direction that appears clockwise when viewed from the high above the $xy$-plane.

How do I even find the path for starters... after that it is straight forward.

I know what the sphere would look like in the xyz plane but not the cylinder. How do you sketch the cylinder?

simultaneous equations?

Ok so subbing in the cylinder equation the way it is written to the sphere gives x+z^2=1 which would some kind of parabola. What variable do you rearrange this new equation to?

some parametric representation
when you need the parameter ends
start and finish for t

So so if we rearrange it to x=1-z^2, so let r(t)=1-t^2 but I have no idea how to find the limits...

Posted from TSR Mobile

I need to look at the question in detail (sometime tomorrow afternoon) as I am in the middle of my own work and also helping another individual.

atsruser is around and can help you at present.

Ok ill try PM him

Posted from TSR Mobile

he replied to your post

Turns put he's busy too. Damn oh well.

Posted from TSR Mobile

Turns put he's busy too. Damn oh well.

Posted from TSR Mobile

I am looking at the question now

Thanks please let me know

Posted from TSR Mobile

Thanks please let me know

Posted from TSR Mobile

very hard to picture



definitely I am too tired to complete this tonight

do you know what the answer is meant to be

I actually don't. Thanks please look at it when u can.

Posted from TSR Mobile

I actually don't. Thanks please look at it when u can.

Posted from TSR Mobile

I got an answer of pi/4

if my initial modelling is correct (parameterization of the path) then it is all correct.

How did you find the path though?

I will attach my attempt and by no means solution ...

IMG_0001.pdf