Monday 18 September class (Updated)

 

 

Topics:

• Some more on integration by parts: Integrating by parts after a substitution; definite integrals that use integration by parts. (Examples 165 and 166)

• Trigonometric integrals of the form \int \sin^{m}(x)\cos^{n}(x)\textrm{d}x with m and n positive integers.

These integrals can become rather long as we see, so keeping track of terms and signs is very important.

Here are some nice videos on trigonometric integrals from PatrickJMT: Highly recommended to view even before we discuss in class!

Trignonometric integrals part 1 of 6 

(what we did today, for \int \sin^{m}(x)\cos^{n}(x)\textrm{d}x when at least one of the powers is odd)

 

Trignonometric integrals part 2 of 6 

(what we did today, for \int \sin^{m}(x)\cos^{n}(x)\textrm{d}x when both powers are even)

 

Trignonometric integrals part 3 of 6 

(Similar to what we did today, but for \int \tan^{m}(x)\sec^{n}(x)\textrm{d}x which works a similar way)

Trignonometric integrals part 4 of 6 

(More examples of \int \tan^{m}(x)\sec^{n}(x)\textrm{d}x)

 

Trignonometric integrals part 5 of 6 

(Integrating \int \sin(mx)\cos(nx)\textrm{d}x)

Trignonometric integrals part 6 of 6 

(More examples of different kinds of trig integrals that don’t fit neatly into the above categories)

Homework:

• Review the examples discussed in class, and at least the first two videos above.

• Do the WeBWorK:  please do not wait to the last minute! There are two assignments: Integration by Parts 2, and Trigonometric Integrals. You should try at least to do the problems in Trigonometric Integrals which are like the examples we worked in class.

• The quiz on Monday will be on Substitution and Integration by Parts.

• Try to watch the other four videos also, before next time. It will help make the lesson go more smoothly! (I hope)

• Don’t forget that Test 1 is scheduled for the first hour or so of class on Wednesday 27 September. The review self-test and answers will be in a separate post. Please check the course policies on tests.

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!