Finding Scalar Function G: Step-by-Step Guide

[shermaine80]

Hi,

I got a doubt question for this.
Given this general expression for the scalar function, G such that
del G = F(x,y,z)=2xyi + (x^2 - Z^3)j + (-3yz^2 + 1)k

How do i go about finding G?

 

[tiny-tim]

Hi shermaine80!

(have a nabla: ∇ and a curly d: ∂)

If ∇G = fi + gj + hk, then ∂G/dx = f, ∂G/dy = g, ∂G/dz = h,

so G = ∫fdx + A(y,z), G = ∫gdy + B(x,z), G = ∫hdx + C(x,y),

where A B and C can be any functions …

if you try it, you'll soon find it's fairly obvious what A B and C have to be!