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Don't have my book or audio? You can download a free sample of my book and audio lectures containing Lessons 1 and 2: Did you read my tips on how to study and learn this course? If not, here is a link to those important suggestions: The department posted SOLUTIONS for Assignment 1 (these are not my solutions). Click here.The department posted SOLUTIONS for Assignment 1 (these are not my solutions). Click here.Here is a link to the actual assignment, in case you don't have it: Study Lesson 1 (Inverse Trigonometric Functions), Lesson 7 (Integrals of Trigonometric Functions), Lesson 8 (Integration by Parts), Lesson 9 (Integrating by Trig Substitution), and Lesson 10
(Integrating Rational Functions) from my Calculus 2 book to prepare for this assignment.
BE WARNED! The integrals on this assignment are very challenging. They keep combining two or three techniques into one question, so you must thoroughly study Lessons 4, 7, 8, 9, and 10 before attempting questions 3-13 in the assignment. Knowledge of only one technique will only lead to
confusion.
Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment. Learn first, then put your learning to the test.
Similar to my Lesson 1, #1. Remember, inverse sine and inverse tangent can only give answers between -π/2 and π/2. inverse cosine can only give answers between 0 and π.
I don't really have examples like this one in my book. Implicit differentiation is something taught in Math 1500. If you have my Intro Calculus book, it is Lesson 6. What you must remember is that you "d/dx" both sides (i.e. do the
derivative with respect to x). But, everytime you do the derivative of a y function with respect to x, that is what I call "illegal," so you must compensate by multiplying the derivative by dy/dx. Then you isolate dy/dx algebraically.
Integration by Parts, similar to my Lesson 8, #1(a) and (b). But, you also have a bit of Lesson 10 coming into play, so make sure you have practiced all of Lessons 7 to 10 in my book before attempting any of the integrals on this
assignment. They are mixing things up pretty good.
Integration by Parts, similar to my Lesson 8, #1(c).
Integration by Parts, similar to my Lesson 8, #1(c). There will also be a pretty fancy u substitution afterwards.
Study all of Lesson 7 to prepare for this integral.
Study all of Lesson 7 to prepare for this integral.
You will be using complete the square here (see my examples in Lesson 4 and Lesson 9). See Lesson 9, #1(f) for an example of the method, if not the same integral.
Polynomial long division! See Lesson 10, #1(a) and (b).
This is a u substitution trig integral from Lesson 7 combined with a rather horrible partial fractions integral from Lesson 10. Will eventually turn into something like Lesson 10, #1(f).
Method 1: Use the identity cos(2x) = 1 - 2sin^2 (x).
Method 2: Use the identity cos(A)sin(B) = 1/2 [sin(A+B) - sin(A-B)].
I think the best thing here is to let u = sqrt(x), then u^2 = x, and 2udu = dx. Still a lot to do after that.
Integration by Parts, similar to my Lesson 8, #1(h).
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