After completing this section, students should be able to do the following.Know the definition of a frustum.Know how to compute the surface area of a frustum.Set-up an integral to compute the area of a surface of revolution in terms of xx.Set-up an integral to compute the area of a surface of revolution in terms of yy.Compute the area of a surface of revolution.

After completing this section, students should be able to do the following.Use reduction formulas and the Pythagorean identity to compute integrals involving trigonometric functions.Recognize the patterns that appear in trigonometric integrals, and use appropriate substitutions to compute them.Compute integrals involving powers of sine and cosine.

After completing this section, students should be able to do the following.Use Pythagorean identities to simplify expressions.Substitute trigonometric functions to simiplify integrals.Complete the square to change the form of an integral. 

After completing this section, students should be able to do the following.State the definition of a vector.Calculate the magnitude of a vector.Work with vectors in two or three dimensions.Multiply vectors by scalars.Add and subtract vectors.Find unit vectors.Use vectors in applied settings.

After completing this section, students should be able to do the following.Identify real numbers.Compute the distance between points.Find the equations for planes.Give the equation for a circle.Give the equation for a sphere or ball.