Today we learned a short cut (tabular integration) to use when we have to integrate by parts repeatedly. Now you should be able to complete the homework that was assigned on Friday p. 328 #1,2,3,5,7-14, 19, 20. Solutions available in the google folder. Make sure you are memorizing your integrals and trig identities!
Unfortunately I did not try the problems before assigning them to you on Friday. Many of the problems require you to use integration by parts repeatedly to solve the problem. There are shortcuts that we did not cover yet. For Monday try to do problems #1,2,3,5 only. Numbers 2 and 5 require you to do integration by parts twice. If you are careful with your work and your signs, you should be able to do the problems.
Today we practiced using integration by parts to evaluate integrals. Homework is p. 328 #1,2,3,5,7-14, 19, 20
Today we learned a new technique for integration - integration by parts. Homework is a worksheet (only 9 problems!). Most of you are getting the concept, but many of you are forgetting to use the chain rule in the interim steps!
If you missed class today, check out this video on youtube. Today we reviewed integration by substitution for both indefinite and definite integrals. We also learned how to solve separable differential equations. Homework is p. 321 #1-27odd, 31-37odd, and 39, 43. Skip #5 - it involves an integral of an inverse trig function, which we did not memorize. Solutions are posted in the google folder.
Today we reviewed the concepts of differential equations and initial value problems, and definite and indefinite integrals. We also learned the rules for 2 new integrals (1/x and e^x). Please, please, please work on memorizing the basic integration rules that you have. It will truly make your lives easier as we learn new techniques for finding integrals. Homework is p. 312 #7-24, 31-34, 39-41.
The solutions manual (chapter 6) is available here. Today we worked on test corrections for the basic integration test. You also have a worksheet for homework. There are 4 integration problems in each row. You need to determine what method of integration you would use in each case (options are 1) substitution 2) algebra or trig identity 3) nothing needed, the antiderivative is obvious or 4) can't be done with the techniques I have learned so far. There should not be more than one problem that can't be done in each row. If you have more than one "can't be done" per row, you have done something wrong. Go back and figure it out! Solutions will be posted tomorrow after we go over the answers in class.
NOTE: No Graphing Calculator on the test tomorrow. I will have scientific calculators available tomorrow for you to use!
Solutions for the review assignment have been posted in the google folder. There are a few problems at the end that I didn't get to finish because I ran out of time. Sorry!! Today we completed a review assignment to prepare for the test tomorrow. Solutions are in the google folder.
Today we practiced using substitution to integrate trig functions. Then we talked about using substitution to evaluate definite integrals. Homework is worksheet 4-5 #43-56, 75, 76, 81. Don't forget to change your limits of integration when you evaluate a definite integral using substitution. Solutions are posted in the google folder. Note: #76 has an imaginary number as an answer.
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