This is a sample, and is meant to represent the material usually covered in Math 9B for the final. An actual test may or may not be similar.
Click on the boxed problem numbers to go to a solution.
Divide the interval into four subintervals of equal length and compute the left-endpoint Riemann sum of
Evaluate the following integrals.
The population density of trout in a stream is
where is measured in trout per mile and is measured in miles. runs from 0 to 12.
(a) Graph and find the minimum and maximum.
(b) Find the total number of trout in the stream.
Find the volume of the solid obtained by rotating about the -axis the region bounded by and
Find the following integrals.
Find the following integrals
Does the following integral converge or diverge? Prove your answer!