Today we went over some of the more difficult homework problems. May of them required you to use a trig identity to simplify the integral before you could find an antiderivative. Make sure you know the trig identities. It will make your life easier. Really. Homework was a mixed review. You need to decide what method to use to find either area between two curves (integrate w/r/t x or w/r/t y) or to find the volume of a solid (discs or washers). The assignment and answers are attached. (answers are after the assignment.)
Today we practiced some more disc and washer problems. Homework is p. 392 #14.16.21.23.25,27,30,34 due tomorrow. The solutions manual is linked in a previous post.
Here are some videos for discs and washers: Video explanation with example Example 1 video Example 2 video Today we did a short "status check" to see how everyone was progressing with the volume problems. We decided that we needed one more day to practice finding volumes using the disk method. No new homework tonight.
Today we did some more practice problems finding volumes. You should be able to calculate the volume of a solid of revolution created by revolving about EITHER the x-axis or the y-axis, as well as revolving around an axis that has been shifted up/down or left/right. Homework is a worksheet. Solutions are in the google folder.
Today we built models of solids that are created by revolving a function around the x-axis. You then used the models to estimate the volume of the solid. If you did not finish Friday's homework, you should complete it tonight. P. 381 #31-36
Today we learned how to integrate with respect to y, and also how to find the area enclosed by intersecting curves. Homework is p. 380 #4, 9, 10, 11, 14, 18, 21, 25, 27, 30.
Today we learned how to calculate the area between two curves. Homework is p. 380 #1-3 and 5-8. Note: you will need to use trig identities to solve some of these integrals. Also, on #3, the equations are written as functions of y, you need to rewrite the equations as functions of x, then set up the appropriate integral. Tomorrow we will learn an easier trick to solve this type of problem.
Today we applied integration to problems involving work, force and consumption. Homework is p. 372 #21,22,29,30
Today we used physics applications (distance, displacement, velocity) to see how integrals help us to add up many small changes to determine the net change. Homework is p. 371 #1-9 odd. Be careful with signs! The textbook solutions manual for Chapter 7 is available here. I will try to post my solutions by tonight.
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