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Did you read my tips on how to study and learn Math 1700? If not, here is a link to those important suggestions: Did you see my tips for Assignment 1? These are tips for the first assignment in the Distance/Online Math 1700 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course. These assignments are very good (and challenging) practice.
It is possible that you are doing the topics in a different order in the classroom lecture sections, so you may need to wait until later before tackling this assignment. Here is a link to the actual assignment, in case you don't have it: Note that you need to study Lesson 5 (Area Between 2 Curves), Lesson 6 (Volumes), Lesson 7 (Integrals of Trigonometric Functions), and Lesson 8 (Integration by Parts) from
my Calculus 2 book to prepare for this assignment! I think you should find this assignment fairly straightforward if you do thoroughly study and do all the Practise Problems I give you in these lessons.
Don't have my book or audio lectures? You can
download a sample containing some of these lessons here:
Review Lesson 1 in my book if you need assistance graphing and finding the points of intersection for the trig function. Be careful, you should discover there are two separate regions of area, so you will need to set up two
integrals.
This question is quite similar to my Lesson 4, question 1(a). It even has the same three points of intersection! Try plotting a few more points perhaps, like x=2, -2, 3, -3, to get a feel about how to sketch the sine curve.
This is quite similar to my Lesson 6, question 1(a). To sketch the graphs, just plot the endpoints of each section. Obviously, you will need to compare your two answers to see which volume is larger. If necessary, use a calculator, but try not
to.
This is quite similar to my Lesson 6, question 2. To sketch the graph, just plot the endpoints of each section. Be careful to find both the x and y coordinates of your points of intersection and use the correct numbers. A "dx" integral requires the x
values for endpoints. A "dy" integral requires the y-values for endpoints.
Note that you do not have to solve the integrals. You are told to just set them up. My question 3 gives you examples of what that means. Literally, just get everything into your integral, and don't forget your endpoints, and you are done.
The integrals are actually quite easy to solve, so you should do them anyway for
practice and as a check on your work. You had better get the same answer for the volumes in (a) and (b)! After all, you are using two different methods to solve the exact same problem.
These integrals are all pretty straightforward if you have studied Lessons 7 and 8 of my book.
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