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), Lesson 4 (The Method of u Substitution), and Lesson 5 (Area between Curves) 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, 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:

This question plays with the concept that a definite integral can be interpreted as the area between the curve and the x-axis as I discuss in Lesson 2, page 41.  The endpoints of the definite integral are vertical lines marking the left and right boundaries of the region.  However, regions below the x-axis are considered negative areas!

Simply, shade the region being described by the integral and find the area by basic geometry.  The regions will be just triangles and rectangles.

This is a review of the various Differentiation Rules as taught in my Intro Calculus book.  Note that I do summarize all the various rules on page 2 of my Calculus 2 book.  Part (a) is using the Fundamental Theorem of Calculus, as discussed in question 2 of Lesson 2 of my Calculus 2 book.  However, parts (b), (c), and (d) all require knowledge of Log and Exponential Derivatives, so you may want to review Lesson 8 of my Intro Calculus book if you have it.  You will especially need to review Logarithmic Differentiation , as taught starting at question 1(n) in Lesson 8.  I am not really sure why they are giving you such tough log derivatives.  It isn't really something that comes up very much in this course.

You should be able to guess what the answer to part (a) of this question is if you have memorized your Elementary Integrals listed on page 1 of my book.  Make sure you do memorize all the Elementary Integrals immediately!  It is impossible to progress in this course if you do not know them.

Part (b) is then applying the Definition of the Definite Integral as discussed in Lesson 3 of my book.  Especially look at my question 4 for examples of what they are getting at.  They are actually making it easier than my examples.

Although it is not required for all these integrals, you will need to learn how to do u substitution (Lesson 4 of my book) before you are ready to do this question.

This is similar to my question 1(g) and (h) in Lesson 2 of my book.

You should study Lesson 5 of my book before you tackle this question.

This question is playing with the idea of changing endpoints when doing u substitution for definite integrals (something I don't find useful).  Generally, as happened in question 4 of your assignment, if you need to use u substitution for a definite integral, I find it easier to ignore the endpoints at first.  In other words, pretend you have an indefinite integral to solve.  Use your u substitution and get the integral solved.  Now that you know the solution to the integral, return to the original definite integral and evaluate your solution between the two endpoints.

However, that approach is not possible here because you are dealing with an unknown function f , so you cannot actually solve the integral.  You can merely relate it to the given definite integral.  Use u substitution and change the endpoints.  Which is to say, if you have a "dx" definite integral with endpoints of 2 and 5 (for example).  That means it is from x = 2 to x = 5.  However, if you are using u substitution to change the problem into a "du" integral, you can then change the endpoints to their corresponding u values.  For example, if you had said that u = 5x, then when x=2, u=10, and when x=5, u=25.  You would then have a "du" definite integral with endpoints of 5 and 25.