Did you read my tips on how to study and learn Math 1700?  If not, here is a link to those important suggestions:

Did read my tips for Assignment 1? If not, here is a link to those important suggestions:

These are tips for the second 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 2 (The Fundamental Theorem of Calculus), Lesson 6 (Volumes), Lesson 7 (Trig Integrals), 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.  However, do note that there is an additional set of Trig Identities you have to memorize as I discuss below.

Don't have my book? You can download a sample containing some of these lessons here:

You should study Lesson 6 in my book to prepare for this question.  Note that you are expected to solve each question both ways.  That also acts as a check on your work.  If you get the same answer for part (a) using the Shell method that you also got using the Washer method, you are likely to be correct.  Ditto for part (b).  This is similar to what I do in my question 2 in Lesson 6.

Yet another Lesson 6 question.  Note that my question 3 in this lesson illustrates how much (or little) you need to do when you are setting up an integral but not solving it.  Make sure you use a test point between the two endpoints to confirm you are getting a positive value for the integral.

Yet another Lesson 6 question.  Note that my question 3 in this lesson illustrates how much (or little) you need to do when you are setting up an integral but not solving it.  Make sure you use a test point between the two endpoints to confirm you are getting a positive value for the integral.

Yet another Lesson 6 question.  Note that my question 3 in this lesson illustrates how much (or little) you need to do when you are setting up an integral but not solving it.  Make sure you use a test point between the two endpoints to confirm you are getting a positive value for the integral.

You need to study Lessons 7 and 8 in my book to prepare for this question.

5(a) is standard integration by parts.  Look at how I do my question 1(d) in Lesson 8 as an example of how to deal with a definite integral.  My preference is to solve the indefinite integral first, then return to the definite integral to complete the problem.

5(b) is similar to part (a) but you have to get rid of the absolute value first.  Look at my question 1(h) back in Lesson 2 for an example of how to deal with an absolute value in an integral.  You need to break this integral up into two separate integrals based on where |x| = x and where |x| = -x.

5(c) is another standard integration by parts integral.  Note that arcsinx is inverse sinx.  Similar to my 1(c) in Lesson 8.

5(d) is yet another integration by parts.

5(e) is a classic trig integral like I teach in Lesson 7.

5(f) is a classic trig integral like I teach in Lesson 7.  More than one way you can solve this one.

5(g) is a classic trig integral like I teach in Lesson 7.

5(h) is a type of trig integral that is not covered in my book.  For integrals of this type, you need to use another family of trig identities.  Click this link for a handout explaining the identities you need to know:

Math 1700 Trig Product Identities

5(i) is proven using integration by parts.  Here is a hint:

I give you the Average Value formula for integrals back in Lesson 2.