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Material Type: Exam; Class: Calculus II; Subject: Math; University: Portland Community College; Term: Winter 2009;
Typology: Exams
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Work each of these problems entirely by yourself.
Do not get help from any person on any of these questions.
Do not get help from any person on any question that is essentially the same as any of these questions.
Do not compare your answers or work with any other person’s answers or work.
Do not have any other person look over your work or check your answer.
You may look at your notes and textbook while working these problems. Remember, though, that there will be questions like these on your final exam and you will not have notes or a textbook to look at while taking your final exam. The exception to the later statement is that your final will include area questions rather than volume questions.
calculations and that you state your conclusion using the unit of Joule.
⎛ π ⎞
and
⎛ π ⎞
. Find the volume of the solid that results from revolving the outlined
illustrated in class.
Figure 1
Write down the disk method inspired improper integral that would compute the resultant solid’s volume and then write down the improper integral that would compute the solid’s surface area.
Evaluate each integral on your calculator and write down the somewhat surprising results. In
You do not need to include fancy labels on this problem – just give me the integrals and answer.
2
b
Figure 3
the curve that look quarter-circular are indeed
[1,8 ]^. Make sure that your reasoning is clear.
Figure 4