Need help with this question, topic is about potential and vectors

[raw galleon]

need help understanding how to go about solving something like this

[tribal dock]

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[raw galleon]

@sonic nimbus

[sonic nimbus]

Hell naw I ain't integrating allat.

[raw galleon]

HAHA

i just need to know how to do it lol

[mossy cape]

This is beyond my knowledge

Let's ping calc helpers

<@&727457725017096242> :3

[raw galleon]

Yeaaaaa. theres a series of 3 questions like this that i sorta need to understand,

[mortal mural]

If F is conservative, it means that there is a potential V so that
-grad(V) = F

So you essentially integrate F
It should be like V=-(sin(4yx)+4z^3*y^2+C)

I am sorry that I can't write it in Latex😅

Now you want that if x=y=z , then V=0
And with that you calculate the constant C

Oki, maybe don't name it C cause for you, C is the path for circulation haha

Now, to calculate the integral, you use the dot product between F(r(t)) and the derivative of r (which is dr/dt= 1/Pi, -3sin(t), 3cos(t)).

And then you integrate for t

Note that here, it is F(r(t)) instead of F(x,y,z)

For that, you simple change x to t/pi , y to 3cos(t)+4 and z to 3sin(t)+4 and put this stuff in F

The integration limits of integral of (F(r(t))•dr/dt)dt are 0 and 3pi/2