Suppose f⃗ (x, y)=−yi⃗ +xj⃗ and c is the line segment from point p=(5,0) to q=(0,4).

(a) find a vector parametric equation r⃗ (t) for the line segment c so that points p and q correspond to t=0 and t=1, respectively. r⃗ (t)=
(b) using the parametrization in part (a), the line integral of f⃗ along c is ∫cf⃗ ⋅dr⃗ =∫baf⃗ (r⃗ (t))⋅r⃗ ′(t)dt=∫ba dt with limits of integration a= and b=
(c) evaluate the line integral in part (b).
(d) what is the line integral of f⃗ around the clockwise-oriented triangle with corners at the origin, p, and q?
hint: sketch the vector field and the triangle.