9.1: 6* In exercises 1-12, sketch the plane curve defined by the given parametric equations and find an x-y equation for the curve. 6. (x = 2 -t ly = tz + 1 9.2:4 4. Explain why the sign (+) of " y(t)x'(t) dt in Theorem 2.2 is different for curves traced out clockwise and counterclockwise. THEOREM 2.2 (Area Enclosed by a Curve Defined Parametrically) Suppose that the parametric equations x = x(t) and y = y(t), with c s t s d, describe a curve that is traced out clockwise exactly once and where the curve does not intersect itself, except that the initial and terminal points are the same [i.e., x(c) = x(d) and y(c) = y(d)]. Then the enclosed area is given by A = ( y(x' ()at = - [ x(by(1 ) at . (2.4) If the curve is traced out counterclockwise, then the enclosed area is given by A= - y(x()at = x()y() di. (2.5)