Exam 18: Fundamental Theorems of Vector Analysis

Find the flux of the vector field through the boundary of the region Assume the boundary is oriented with outward-pointing normal.

Let where and . Compute for .

Use Green's Theorem to calculate the counterclockwise circulation of the vector field around the boundary of the region that is bounded above by the curve and below by the curve

Evaluate where is the triangle with vertices and , traversed in a counterclockwise direction.

Find the circulation of the field around the boundary of the region that is bounded above by the curve and below by .

Evaluate where is the ellipsoid oriented outward, and

Evaluate where c is the closed curve traversed in a counterclockwise direction.

Compute the area of the region bounded by the curve

Compute where is the curve of intersection of the sphere and the plane .

Calculate the circulation of the vector field around the circle oriented counterclockwise.

Let where C is the circle of intersection between the sphere and the plane , and . The value of is which of the following?