ST 552

Calculus on a Computer

Assignment 13 – More Applications

1. Set up and evaluate the integrals to find the arc length of from (1,1) to (3,27) by integrating with respect to

a. x, and

b. y.

2. Set up three integrals to evaluate the circumference of a circle – integrating with respect to x, y, and a parameter . Which looks easiest? Evaluate that one.

3. Find the surface area of a cone using a surface area integral.

4. Repeat problem 3 for a sphere.

5. Find the circumference of the ellipse Use a parametric equation.

6. Find the surface area, and the volume, of the solid formed by rotating the area between and the x-axis, about the x-axis.