Math 1700 Distance: Revised Tips for Assignment 2

Published: Sat, 01/26/13


 
A student has pointed out that question 4 actually says the same function twice.  That makes the question much easier.  It is just the area between two curves, not three as I originally thought.
 
Please note that I am now taking registrations for my midterm exam prep seminars.  Please click this link for more info and to register, if you are interested:
Grant's Exam Prep Seminars 
 
Did you read my tips on how to do well in Math 1700 Distance?  If not, here is a link to those important suggestions:
How to do Well in Math 1700 Distance 
 
Tips for Assignment 1
Even if you are not taking the distance course, I think it is very useful for all Math 1700 students to attempt these hand-in assignments.  In general, the assignments can be quite demanding and really force you to solidify your math skills.  However, the fact is that the distance course covers the topics in a different order from the classroom lecture sections, so I would not advise classroom students to look at this assignment until they have studied the relevant lessons in class.
 
Here is a link where you can download a copy of Assignment 2:
Math 1700 Distance Assignment 2 (Jan 2013) 
 
Note that you need to study Lesson  4(The Method of u Substitution), Lesson 5 (Area between Two Curves) and Lesson 6 (Volumes) 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. 
 
Don't have my book? You can download a sample containing two lessons here (unfortunately, the sample contains lessons 1 and 11):
 
Question 1 is integration obviously.  Hint: you will use u substitution for some but not all of these three integrals.  If you do use u sub to solve part (c), make sure you don't actually use u because that variable is already in the problem.  You will have to use a different letter.
 
Question 2 is more of the same, but this time they are definite integrals.  Some people change the endpoints to u values if they are using u substitution to solve a definite integral.  I do not advise this.  I suggest, that you write down the indefinite integral first and solve it.  Then, return to the definite integral and sub the endpoints into your solution.
 
Question 3 is  not an integral problem.  You cannot use methods of integration to solve it.  First, separate the problem into two different integrals by splitting the 3 term away from the square root term.  Now draw a graph of each of these two functions for the region between -2 and 2.  (Draw a graph of y = 3 and a separate graph of y = square root of (4 - x2).)  You should now be able to compute the area between the graph and the x-axis from x = -2 to x = 2 in each case using basic geometry (area of a rectangle, area of a circle).
 
Question 4 is like my questions in Lesson 5. It is just a typo that the first graph is listed twice, so this is classic area between two curves.
 
Question 5 is like my questions in Lesson 6.
 
Question 6 is using the average value formula that I mention at the top of page 4 in my book and I think shows up as one of the homework questions in Lesson 2.  Be sure to notice that the formula uses minutes as its unit for time in your problem.