Evaluate∫ xdx + xydy where c is the line y = 1 - x for 0 ≤ x ≤ 1.
(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.
i understand as far as substituting x(t) = sin t, y(t) = 1 - sin t, dx = cos t dt and dy = (- cos t) dt into the equation with limits of t = 0 to t = pi/2 but i dont know how to integrate sin t cos t or the other part? do i need to use the product rule??