Y'= cosx under the radical sign, so the arc differential ds= {1+ (cosx under the radical sign) 2} dx = (1+cosx under the radical sign) 2} dx =

Please note that when x changes from -pai/2 to pai/2 curve, the full length will be obtained, and the required curve length is

S= definite integral (from -pai/2 to pai/2) (1+cosx)dx= definite integral (from -pai/2 to pai/2) [2 COS 2 (x/2)] DX = 2 * definite integral (from -pai/2).