A closed curve is a curve for which the initial point is the same as the final point. A simple closed curve (orJordan curve) is a closed curve that does not intersect itself. If C is a simple closed smooth curve in R2, thenthe total curvature of C is defined to be R L0 ds, where is the curvature along C and L is the length of C.(a)[2p] Find the total curvature of the ellipse C with equation x2a2+ y2b2=1.Hints. Method 1: Use the polar angle to find a parametrization of the curve C, find the curvature as function of , and then write the total curvature as a definite integral in . Method 2: Show that thecurvature of a plane curve is =|d/ds|, where is the angle between T and i.(b)[1p] What is the total curvature of any smooth simple closed plane curve? Justify your answ