Post date: Oct 15, 2017 9:37:58 PM
We are now learning how we apply all of the antiderivatives we've learned to find.
Friday, 10/13 - we are laying some foundational knowledge for what we'll be learning in a few days. We developed the idea of finding the area under a curve (finding the area of a weird-shaped piece of farmland) by splitting the shape up into very thin rectangles and adding them up. Here is the worksheet from class, and your HW, which is on the last page.
Monday, 10/16 - we continued to develop the idea of area under a curve and saw how this idea of area works with the idea of an antiderivative, tied together by the Fundamental Theorem of Algebra. Here is the worksheet from class. Your HW is to, by 5PM on Monday 10/23, go to this Google Form and submit your idea for your topic for your Math Exploration: goo.gl/6tqMPY
Tuesday, 10/17 - we used the Fundamental Theorem of Calculus to evaluate definite integrals. Here are the slides from class (including instructions on how to use your GDC to evaluate definite integrals). Your HW is p. 807 (Ex. 16.4) #1-10 (check on GDC).
Wednesday, 10/18 - we looked at and proved some properties that are true about definite integrals. Here are the slides from class. Here is the worksheet from class that includes all the properties we can use now for definite integrals. Your HW is also on the worksheet, on the back at the bottom.
Thursday, 10/19 - we looked at more difficult definite integrals that use substitution to find the antiderivative. We also talked about strategies we can use to find the actual areas of regions bounded by the x-axis. Here are the slides from class. Here is the worksheet that follows the class notes. Your HW is p. 807 (Ex. 16.4) #23-27.
Friday, 10/20 - we found the area between two curves. Here are the slides from class. Your HW is p. 818 (Ex. 16.6) #1, 4, 5, 7, 8. Also, your HW is to, by 5PM on Monday 10/23, go to this Google Form and submit your idea for your topic for your Math Exploration: goo.gl/6tqMPY
Monday, 10/23 - we found the volumes of solids of revolution. Here are the slides from class. Your HW is p. 825 (Ex. 16.7) #1-4, 9. Also, your HW is to, by 5PM tonight, go to this Google Form and submit your idea for your topic for your Math Exploration: goo.gl/6tqMPY
Tuesday, 10/24 - we found volumes of solids of revolution with holes in them (the "washer" method, as opposed to the "disc" method). Here are the slides from class. Here is the worksheet from class, which includes your HW, which is p. 825 (Ex. 16.7) #10, 12, 13, 19.
Wednesday, 10/25 - we found areas and volumes where it is easier to consider a function of "y" instead of a function of "x". Here are the slides from class. Here is the worksheet of problems from class, which includes your HW, which is p. 818 (Ex. 16.6) #13, 14. For a challenge, you can try p. 825 (Ex. 16.7) #21.
Thursday, 10/26 & Friday, 10/27 - we practiced finding areas and volumes. Here are the slides from class. Here is the worksheet of problems from class. For HW, try some of these problems for about half an hour. Here is an explanation for the solution to #24 on the backside of the HW sheet.