College Assignments/Image:Test Ana-IV.odt

B.Sc.(Hons.) Mathematics â€“ III year Test Analysis â€“ IV Time: 1Hr. Max. Marks: 25 (This question paper consists of 6 questions. All questions carry 5 marks each.) (Attempt any 5 questions.)
 * 1) By changing the order of integration, prove that [[Image:]] # State Greenâ€™s Theorem and verify it for I = [[Image:]] Where C is the closed curve formed by y3 = x2 and y = x between (0, 0) and (1, 1). # Use the transformations [[Image:]]to evaluate [[Image:]] over the region common to the circles x2 + y2 = x, x2 + y2 = y. # Evaluate [[Image:]]; m â‰¥ 1, n â‰¥ 1, p â‰¥ 1 where E is the region bounded by x = 0, y = 0, x + y = 1. # Evaluate: [[Image:]] by using x = r Cos2Î¸, y = r SinÎ¸ CosÎ¸. # Evaluate: [[Image:]], over the region bounded by x y = 1, y = 0, y = x and x = 2.