Note that you need to study Lesson 1 (Inverse Trigonometric Functions), Lesson 2 (The Fundamental Theorem of Calculus) and Lesson 3 (Riemann Sums) 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 two lessons here (unfortunately, the sample does not contain lessons 2 and 3, but lessons 1 and 11):
Question 1 is like my question 1 from
Lesson 3. You may want to use a calculator to help you plot the points you calculate in order to draw the graph but, as they request, make sure you state the exact values in your calculations and when you label your points on the graph.
Question 2 is like question 3 in my Lesson 3. Although it was not said explicitly, they mean the area under the given curve, but above the x-axis.
Question 3 is just another way of asking question 2.
Question 4 is like my question 1 in Lesson 2. However, an eagle-eyed student has noticed that question 4(c) is an improper integral
because the function is undefined at y=0 which is between -1 and 2 (the
endpoints). There is no way they meant that. Improper integrals are
too advanced for this stage of the course. Please contact the prof and
make him aware of this issue and I expect the question will be revised. If it is not revised, you should point out exactly what I am saying here, and say that you cannot solve this integral at this stage because it is improper.
