(1 point) Find the line integral with respect to arc length / (4x + 5y)ds, where C is the line segment in the xy-plane with endpoints P = (6, 0) and Q = (0, 5). (a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond to t = 0 and t = 1, respectively. (b) Using the parametrization in part (a), the line integral with respect to arc length is (4x + 5y)ds = [." dt with limits of integration a = and b = (c) Evaluate the line integral with respect to arc length in part (b). ( 4x + 5y)ds =2 2 (1 point) If C is the part of the circle = 1 in the first quadrant, find the following line integral with respect to arc length. (8x - 9y)ds = C{1 point) Consider a piece of wire with uniform density. it is the quarter of a circle in the first quadrant. The circle is centered at the origin and has radius 2. Find the center of gravity (37:, j!) of the wire. zzy: {1 point} Suppose x, 3;) = 2er + xy}. Use Green's Theorem to calculate the circulation of E around the perimeter of a circle C of radius 2 centered at the origin and oriented counterclockwise. f'u: C (1 point) Let C C R be the circle with radius 2 centered at the origin. Let F : R - R be the vector field defined by F(x, y) = (16x, 13). Find the flux of F coming out of the circle through the curve C. JoF . N ds =