I have given an extra hint for question 1(a) below.

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

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? Click here.

Did you see my tips for Assignment 2? Click here.

Did you see my tips for Assignment 3? Click here.

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:

Study Lesson 12 (Improper Integrals and the Comparison Theorem) and Lesson 13 (Arc Length and Surface Area) from my Calculus 2 book to prepare for this assignment.

These are all pretty standard improper integrals as shown in Lesson 12.  You will need to use u substitution to solve most of these integrals, so I suggest you solve the indefinite integral first using u sub, then deal with the improper definite integral only once you know the solution to the antiderivative. 

Note that part (a) requires integration by parts. Note, that one of the terms you get in your answer will require L'Hopital's Rule in order to properly solve the limit.

Hint for part (b): You can pull both factors in that denominator up using negative exponents.  Then u sub should go quite smoothly.

Both parts (b) and (c) will have to be split into two separate improper integrals before you can solve them.

I don't anticipate any real difficulties here if you have studied Lesson 13, question 1.

Hint for part (a): Rewrite the negative exponent as a denominator and get a common denominator inside the square root.  Then separate the top from the bottom as separate square roots.  You can actually square root the bottom and then u sub will work.

Like my Lesson 13, questions 2 and 3.

Always consider whether to use dx or dy, and if you decide to use dy, make sure you are using the y-values for your endpoints.  Also, if it seems feasible to use either one, always keep in mind that, if you hit a snag, you could always try the other way instead.

Like my Lesson 13, questions 2 and 3.

Always consider whether to use dx or dy, and if you decide to use dy, make sure you are using the y-values for your endpoints.  Also, if it seems feasible to use either one, always keep in mind that, if you hit a snag, you could always try the other way instead.