Topics:

• More on trig substitutions: substituting back at the end, for indefinite integrals

(Example from last time and also the examples below)

• Trig substitutions when there are no radical signs over the sum or difference of squares: I discussed Examples 178-180 in the textbook.

• Completing a square to use a trig substitution (Example 179)

The videos on Trig Substitution from Patrick’s Just Math Tutorials are linked in the post from last time: Example 3 uses completing the square to get to the trig substitution.

• Partial fractions: introduction, and one integral.

Patrick has a video on finding the partial fractions expansion, which unfortunately contains an error (wrong number). See if you can find the error and correct it! (There will be a blue annotation square when the error occurs.)

He also gives a nice trick for finding the coefficients when you only have linear factors in your denominator.

Homework:

• Review the examples discussed in class. I hope you find these videos helpful also!

• Do the WeBWorK: Note there is a new assignment I linked after class: it is just on finding the partial fractions expansions, no integration yet. These are not due until next week, but please do not wait to the last minute! Try to do at least a few by next time.

• There will be a quiz next time: the topic will be Trigonometric integrals of the type that includes powers of tangent and/or secant, and also a definite integral which uses trigonometric substitution.

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!