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

Did you read my Tips for Assignment 2?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 3?  If not, here is a link to those important suggestions:

These are tips for the third 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:

You need to 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.

Don't have my book?  You can download a free sample of my book and audio lectures containing Lesson 1 and 11:

These are all pretty standard improper integrals.  You will need to use u substitution, perhaps, and integration by parts to solve some of the integrals, so I suggest you solve the indefinite integral first, then deal with the improper definite integral.

Classic arc length integrals.  I think you will find both of them easiest to solve if you use dy rather than dx.  Note there is a typo in point P in part (b).  That should read P(1,5).

Classic Surface Area integrals.  They should have made it clear to use the first quadrant region only in part (b), since the symmetry of the graph would have it overlapping itself when it rotates around the x-axis.  Also note, if you choose to use dy in part (b), then you must use y values for your endpoints.

Another basic surface area question.