The answers to the question are given as x²y + 24x +16y and 87
How to solve for the potential function of the vector field
(2xy + 24, x² + 16)
We have to check in order to be sure that the vector that we have here is a gradient field
we have fx = 2xy + 24 and fy = x² + 16
Such that we would have x²y + 24x +g(y)
for f(y) g' = 16 = 16 + c
Given that there is no lose of generality, we are going to have the following where
x²y + 24x +16y
b. We have to solve this oart by making use of the fundamental theory of integrals
f2,4 = 4*4 + 24*2 + 16*4
= 16 + 48 + 64
= 128
f1,1 = 1*1 + 24*1 + 16*1
= 1 + 24 + 16
= 41
128 - 41 = 87
Read more on vector field here:
https://brainly.com/question/14288288
#SPJ1
