48-52.

4852. Ellipse problems Let R be the region bounded by the ellipse xz/a2 + 322le = 1, where a > 0 and b > 0 are real numbers. Let T be the transformation x = am, y = bv. 48. Find the area of R. 49. Evaluate [flxyldA R 50. Find the center of mass of the upper half of R ( y 2 0) assuming it has a constant density. 51. Find the average square of the distance between points of R and the origin. 52. Find the average distance between points in the upper half of R and the x-axis. 25-30. Normal and tangential components For the vector field F and curve C, complete the following: a. Determine the points (if any) along the curve C at which the vector field F is tangent to C. b. Determine the points (if any) along the curve C at which the vector field F is normal to C. c. Sketch C and a few representative vectors of F on C. 3542. Gradient fields Find the gradient field F = V40 for the following potential functions (p. 36. Q X, y = xy