ST 552

Calculus on a Computer

Assignment 12 – Applications of the Definite Integral

1. Set up the volume of a cone as an integral. Evaluate.

2. Set up an integral to find the volume of an equilateral tetrahedron. Evaluate.

3. Consider the solid obtained by rotating the region in the first quadrant between, , and around the x-axis. Set up the integrals for the method of shells, and the method of slices. Evaluate both.

4. The wetted face of a dam is a trapezoid 40 feet wide at the top, and 30 feet wide at the bottom. The bottom is at a depth of 12 feet, and the face is sloped so that the bottom is 5 feet in from the top. Find the total hydrostatic pressure on the face.

5. A water tank is a sphere, 3 m in diameter, the bottom 15 m above ground level. How much work does it take to fill the tank half-way? All the way?

6. Find the total work to put a one ton satellite into geosynchronous orbit. Geosynchronous orbit is approximately 22,240 miles above the surface of the earth. You may assume the earth is a sphere with a radius of 3960 miles. The force due to gravity is proportional to and you know the value at distance from center = 3960.