Exam 17: Line and Surface Integrals

Let be the curve . A) Parametrize using polar coordinates. B) Find the length of

Find the surface area of the surface .

Compute the work performed in moving a particle along the path by the force .

Compute the surface integral where and S is the part of the sphere between the planes and oriented outward.

Find where is the path from to and .

Let denote the closed curve of intersection of the hemisphere and the cylinder oriented counterclockwise. Compute where .

Compute the line integral where C is the segment from to and .

Find a potential function for the field by inspection.

Compute , where is the part of the ellipse joining the point to the point and .

Find where is the path from to and .

Compute where and oriented upward.

Compute the flux of the vector field through the surface of the portion of the paraboloid with outward-pointing normal.

Let . Find a function so that is conservative in and for all .

Compute where S is the part of the plane in the first octant bounded by the planes and

Evaluate where and S is the surface oriented upward.

Let . Express in terms of the unit radial vector in .

Define Compute the vector assigned to the point by the vector field

Let S be the surface above the plane bounded by the sphere from above and by the cylinder at the sides. Compute if

Let C be the curve , , , , and let . The value of is which of the following?

The mass of the part of the cone with and density is which of the following?