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

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 1 (Inverse Trigonometric Functions), Lesson 2 (The Fundamental Theorem of Calculus), Lesson 3 (Riemann Sums), and Lesson 4 (The Method of u Substitution) 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. 

Make sure that you study Lesson 1 of my book first.  Although it is not directly involved in Assignment 1, it provides some key skills (especially the trigonometry review) you will need throughout the course and assignments.

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

They mean that you must use the method of Riemann Sums to solve this question.  I suggest you do this question open-book, following the method I demonstrate in Lesson 3, question 3(a) and (b) to solve this question.  It is highly unlikely that you would ever have to do a question like this on an exam, so it is totally fine to do this one open book.

Note that you can check that your answer is correct by simply solving the definite integral using elementary integrals as taught in Lesson 2.

This is quite similar to my Lesson 2, question 1(g).  To sketch the graph, just plot the endpoints of each section.

This is using the Fundamental Theorem of Calculus as I demonstrate in Lesson 2, question 2.

These are all similar to the questions I do in Lesson 4.  For the definite integrals given in parts (c) and (d), I recommend you first set up and solve the indefinite integral, then use that solution to compute the answer to the definite integral. 

There is a technique where you can change the endpoints of a definite integral if you have done a u substitution, but I find that unhelpful.  Frequently in this course, you will have to use complex methods to solve an integral.  Carrying the endpoints of a definite integral just adds to the complications and can lead many students to lose track or express their solutions erroneously.

A far more prudent approach, is, when given a definite integral, first set up the associated indefinite integral and solve it first, then return to the definite integral and complete your solution.