Integral around half an ellipse
Calculate the integral in each of the following two cases:
1. is the bottom half of the ellipse , traversed from the point (2,0) to the point (-2,0);
2. is the complete ellipse , traversed in the counterclockwise direction.
Also, write the integral as the integral with respect to arc length of the dot product of a vector field with the unit tangent vector to the curve .
I got 0 for both my integrals. The way I did them was parametrize the curve in two different ways (first one using t, second one using ), but they both gave me 0. I am not sure if this should be correct, can someone please confirm? The vector field for the second part of the problem is obviously , right? Is it a trick question?