Two question here please answer it correctly 40. Evaluate f (x2-2xy)dx +(x2y+3)dy around the boundary of the region defined by y2 = 8x and x = 2
(a) directly, (b) by using Green's theorem. Ans. 128/5
(TT.2)
41. Evaluate f (6xy - y2) dx + (3x2 --- 2xy) dy along the cycloid x = 6 - sin 6, y = 1 - cos 6.

Apreheater involves the use of condensing steam at 100°c on the inside of a bank of tubes to heat air that enters at 1 atm and 25°c. the air moves at 5 m/s in cross flow over the tubes. each tube is 1 m long and has an outside diameter of 10 mm. what is the minimum value of nl needed to achieve an outlet temperature of t 75 c? what is the corresponding pressure drop across the tube bank?