Third Midterm-Practice Test
You know the drill.
- Find the volume of the solid that lies under the plane and above the rectangle
- Find the volume of the solid enclosed by the paraboloid and the planes and
- For the integral , sketch the region of integration and change the order of integration.
- Find the volume of the solid enclosed by the parabolic cylinder and the planes
- Use a double integral to find the are of the region inside the cardioid and outside the circle
- Use polar coordinates to combine the sum below into one double integral, and evaluate it.
- A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool.
- The boundary of a lamina consists of the semicircles and together with the portions of the –axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin.
- Express the volume of the wedge in the first octant that is cut from the cylinder by the planes and as a triple integral.
- Evaluate the triple integral where is bounded by the cylinder and the planes and in the first octant.
- Identify the surface with equation in cylindrical coordinates given by
- Evaluate where is enclosed by the sphere in the first octant.
- Find the volume of the part of the ball that lies between the cones and
- Find the Jacobian of the transformation
- By using an appropriate change of variables, evaluate the integral where is the parallelogram enclosed by the lines and