202 PRACTICE MIDTERM 2
Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer. Show your work.
Please answer the following true or false.
If false, explain why or provide a counter example.
If true explain why.
If all six limits of integration of an
integral written in spherical coordinates are constants, then the region of
integration is a sphere.
PROBLEM 2 Set up
integrals to evaluate the following. Use
the coordinate system that will most effectively solve the integral.
The mass of the tetrahedron that lies in the first octant and below the
plane x + y + 2z = 2
such that the density function is f(x,y,z)
The surface area of the part of the paraboloid
z = 9 - x2 - y2
that lies above the plane
z = 5
The moment of inertia about the z-axis of the solid between the cylinders
x2 + y2 = 25
+ z2 = 25 that has density function 1.
order of integration.
A master dart
thrower has determined that her probability density function is inversely
proportional to one more than the fourth power of the distance in centimeters
from the center of the dartboard.
Consider the solid described by
(x + 2y)2 + (2y - 2z)2 + (x + z)2
with density function
f(x,y) = x + 2y
Show that the mass of the solid is equal to