009B Sample Final 3

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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.

 Problem 1 

Divide the interval    into four subintervals of equal length    and compute the left-endpoint Riemann sum of  

 Problem 2 

Evaluate the following integrals.




 Problem 3 

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.

 Problem 4 

Find the volume of the solid obtained by rotating about the  -axis the region bounded by    and  

 Problem 5 

Find the following integrals.



 Problem 6 

Find the following integrals



 Problem 7 

Does the following integral converge or diverge? Prove your answer!