Evaluate∫ xdx + xydy where c is the line y = 1 - x for 0 ≤ x ≤ 1.

c

(a) By using the parameterization x(t) = t^2 & y(t) = 1 − t^2 for 0 ≤t ≤1.

(b) By using the parameterization x(t) = sin t & y(t) = 1 − sin t for 0 ≤t ≤

2Note that one would normally choosex(t) = t & y(t) = 1−t to evaluate this integral, but the above choices are selected to demonstrate that the choice of parameterization does not affect the answer.