Exam 17: Line and Surface Integrals

Compute where S is the surface oriented upward and .

Define At what points is normal to the vector

Evaluate where S is the surface cut from the paraboloid by the planes , and .

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

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

Find the flux of across the surface , oriented outward.

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

Evaluate for the path C shown in the following figure. The path consists of the line segment from (1, 0, 0) to (0, 1, 0), followed by the circular arc in the yz-plane with radius 1 joining (0, 1, 0) to (0, 0, 1).

Calculate the work performed by the force field on a particle that moves in the counterclockwise direction around the quarter circle . Assume that is in Newtons and the unit of distance is the meter.

Find the surface area of the portion of the cone within the cylinder

Evaluate where C is the line segment joining the points and

The area of the surface is which of the following?

Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find .

The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following?

Let A) Compute B) Evaluate where C is the parametric curve from to

Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to

Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to .

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

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

Compute the surface integral where and is the surface of the sphere centered at the origin with radius 4.