[math]Evaluate \int_C \mathbf{F} \cdot \mathbf{dr}.[/math]
[math]\mathbf{F}(x, y) = <\frac{1}{y} - e^{2x}, 2x - \frac{x}{y^2}>, C \ is \ the \ circle \ (x - 5)^2 + (y + 6)^2 = 16, oriented \ counterclockwise.[/math]
The integral becomes tedious even if I parametrize it. it looks like it is impossible to solve it without a shortcut or a trick.
[math]\mathbf{F}(x, y) = <\frac{1}{y} - e^{2x}, 2x - \frac{x}{y^2}>, C \ is \ the \ circle \ (x - 5)^2 + (y + 6)^2 = 16, oriented \ counterclockwise.[/math]
The integral becomes tedious even if I parametrize it. it looks like it is impossible to solve it without a shortcut or a trick.