MediumCalculusca-078

Conservative Potential Value

Problem

The field F(x, y) = [a*x + b*y, b*x + c*y] is conservative because its Jacobian is symmetric.

Find the potential phi with phi(0, 0) = 0 and return phi(x, y) = 0.5*a*x^2 + b*x*y + 0.5*c*y^2.

Hint

Integrate the first component with respect to x, then match the second component.

case 1

in: [2,0,2,1,1]

expected: 2

case 2

in: [4,1,2,2,3]

expected: 23

case 3

in: [0,0,0,5,5]

expected: 0

case 4

in: [-2,3,1,1,-1]

expected: -3.5

Starter codePython

def potential_value(a, b, c, x, y):
    # Your code here
    pass

4 test cases · run your code against them in the editor