Welcome to Mrs. Young's calculus class blog! Each week, I will start a new post. Students, you can write questions for me or chat with each other about how to solve a particular problem. As part of your class participation grade each week, every student must comment at least once to my post or another student's comment. I look forward to spending this year with you. Enjoy!

Sunday, March 4, 2012

Last week of the 3rd quarter!

This week we are going to finish up chapter 7 and all of the new material you will learn in calculus! Section 3 in chapter 7 introduces a very important subject in calculus: integrals as volume in the coordinate plane. There is always a problem about this on the free response section of the AP exam. We have already learned how to use an integral to find the area between curves in the coordinate plane, in 2-D. Volume is in 3-D, though. How do you think that we can find volume in the coordinate plane if the coordinate plane is in 2-D?

Also, watch the video to the right and the first person to respond with the correct answer to the volume problem will get a couple points extra credit. I also do not want your answer in decimal form. Leave it in the most simplified fraction form.
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17 comments:

  1. Elizabeth WhippleMarch 4, 2012 at 11:12 AM

    where is the problem? I watched the video and it said that you have to go to the website to watch the rest of the video. I did but you have to pay to watch it. so im not sure what i am doing wrong

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  2. Mrs. YoungMarch 4, 2012 at 11:15 AM

    The video is a lesson excerpt, but you should see enough to be given a problem that I want you to solve. He does not finish solving it in the video. You probably will not be able to solve it until our lesson in class on Thursday.

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  3. Caroline KangMarch 7, 2012 at 8:07 PM

    We can use cross section area to get volume which we can imagine a shape when we cut in to half or whatever. And using integral, put formula for cross section and find limit. And solve it. Im not sure but i tried to solve that problem and i got 411π/4

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  4. Mrs. YoungMarch 8, 2012 at 4:09 AM

    Caroline, your answer to the problem is not quite correct.

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  5. Krista WoodMarch 8, 2012 at 10:19 AM

    To find the volume of a shape when the coordinate plane is in 2-D you must find out what the shape of the cross section would be and take the integral of the area formula of that cross section shape in the specified interval. The answer to the video above is 382π/15

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  6. Mrs. YoungMarch 8, 2012 at 10:28 AM

    Krista, you're close on that answer to the problem, but not quite. Sorry.

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  7. Krista WoodMarch 8, 2012 at 10:34 AM

    WAIT!! Is it 397π/15??

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  8. Mrs. YoungMarch 8, 2012 at 10:35 AM

    Yes it is. Very good! I will give you the extra credit. Can you try to explain how you got that? We have technically not learned it yet. We will learn it today.

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  9. Anna SchrammMarch 8, 2012 at 12:16 PM

    To find the volume of an object on a 2D coordinate plane, you can either place the object right on the coordinate plane or rotate the object around the x or y axis. In both of these instances, you would find the cross section shape of that object and you would integrate that formula over a certain interval which would give you the volume.

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  10. aiden wangMarch 8, 2012 at 2:42 PM

    3D is one demension more than 2D coordinate plane, so we can solve it using the way we've learned in 2D and cosider the existence of the z-axis. for example, place the object on a 2d plane. what we actually do is give a plate area a hight. and ratate is like give a plate shape a thickness.

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  11. Alexa SpudieMarch 8, 2012 at 8:36 PM

    To find the volume of a shape on the coordinate plane, you can either place it on the plane and imagine it sticking out at you, or you can rotate it about the x or y-axis. In both these methods, you find the area of the cross section and integrate on the interval given to find the volume.

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  12. Alicia WhaJung HanMarch 9, 2012 at 7:06 AM

    There are method to find the 3D volume of object on coordinate plane which is 2D. You have to actually place the object on the coordinate plane and find out the volume of it.Rotating 2D areas, and using cross section to integrate it. So we can find the actual 3D volume of the object.

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  13. Nate LyellMarch 9, 2012 at 8:26 AM

    To find the area of a 3d shape on a 2d coordinate plane you have to visualize revolving the curve around the specified axis and then find the area of a cross section and integrate it.

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  14. Ukbin KwonMarch 9, 2012 at 9:47 AM

    In order to find the volume of a shape that is in 2D, there are few procedures that we have to follow. First of all, we have to see what the shape look like on the graph. Second, rotate x or y-axis and check and see the shape. Finally, we have to integrate it. This is how we can find the 3D volume of the object.

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  15. AnonymousMarch 9, 2012 at 9:49 AM

    To find the volume of an object in coordinate plane, you take a geometric figure to find the volume. You can also rotate about x-axis ans y-axis to make a 3d object. You use the area of cross section and integrate with the interval given.

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  16. christiankMarch 9, 2012 at 10:10 AM

    To find the volume you have to revolve the curve around the axis and then integrate. This makes much more sense when you can see the models.

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