Evaluate the following integral over the ellipse ​

The underlying vector field,

F(x, y) = -y/(4x ² + 9y ²) i + x/(4x ² + 9y ²) j,

is conservative, so any integral of F over a closed path is 0.

To establish that F is conservative, we want to find a scalar function f(x, y) whose gradient is equal to F(x, y), which entails solving

Integrating the first equation with respect to x yields

and differentiating with respect to y gives

if i put something wrong your not gonna like it so rather not say nothing.

no

step-by-step explanation: