Exam 17: Line and Surface Integrals

Determine whether the vector field is a conservative vector field, and if so, find a potential function for by inspection.

Compute along the curve shown in the following figure.

The integral where and with normals pointing to the positive y direction is equal to which of the following?

Compute where and is the path from to .

Let S be the surface . The area of S is approximately which of the following

Evaluate the surface integral where S is the part of the cone between the planes and .

Find where is the path from to and

Find where is the path from to and

Let . Compute where is the segment joining the points and together with the quarter circle centered at the origin and joining the points and . The integration is performed from to .

Let S denote the part of the surface inside the cylinder The area of S is closest to which of the following?

Compute the vector assigned to the point by the vector field

Find a potential function for by inspection.