Two main ideas from today.
A. You are officially responsible for knowing that the derivative of arctan(x) is 1 / (x^2 + 1). This implies that you need to recognize and use
integral of 1 / (x^2 + 1) = arctan(x)+ C
Expect to have to use this on homework, quizzes, and tests.
B. Your general plan of attack for an integration problem is as follows:
1. Do you recognize this as an "easy" antiderivative? For example if you see x^n, sec^2 x, or 1/x - you immediately recognize the antiderivative. Note that all 6 trig functions now fall in this category.
2. If not, then see if you can do algebra to rewrite the problem so that you do recognize it as an "easy" antiderivative. Doing algebra involves expanding (multiplying out), factoring, using trig IDs, log properties or exponential properties.
3. If not, then try a u-substitution to rewrite the problem so that you do recognize it as an "easy" antiderivative. You may have to try several different u-subs.
4. There is no 4. Try 1, 2, and 3 again.
I'll hand out a copy of the test from last year tomorrow in class.
No comments:
Post a Comment