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.
Today was a mental health day. You got your tests back (which were awesome, by the way!). Test corrections (if you choose to do them) are due next Friday. Enjoy the weekend.
Good job! You've been working hard to master integration techniques!
Tomorrow is your integration test. Make sure you know the trig identities. Solutions to the pink worksheet are in the google folder. I still have to do 4 of the problems. If you have questions, email me!
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