Last week we finished 5.3: the Fundamental theorem of calculus (FTC), 5.4: indefinite integrals and 5.5: Substitution method.
The FTC has two parts: part one about the derivative of a special type of functions; part two gives you the third way of computing a definite integrals. (the other two ways being the limit of Riemann sum and net area under curves). Check out problem 68 of section 5.3 for the most general formula for derivatives. This is a good time to review derivatives you learned in 151!
Indefinite integral of a function f(x) is another function. It is the most general antiderivative of f(x). Make sure you review the tables on page 341 and 392. Also review section 4.9! Now to compute a definite integral with the third method (FTC, 2), you first compute the indefinite integral, then evaluate and subtract.
For u-substitution, follow the general tips we summed in class, and whenever you try to make a u-substitution, take its derivative!! That is the best way to tell if you did the right substitution.
Next week, we will finish 5.5: the Substitution method, learn 7.1: integration by parts, then we will review for our first test. I have finished grading your quizzes and will hand them back to you on Tuesday/Wednesday. Remember to regrade if you like some extra points!
Alright, see you on Tuesday!
Reading: 5.5, 7.1 and review
5.5: Read problems 1-6 (no need to write up!); 7,18,27,35,43,46,52,73,75,77
7.1: Read problems 1 and 2 (no need to write up!); 3,5,9,10,23,32,33,37,63,65
Practice tests (to upload)