So you have a function or two or three and then you wrap it around somewhere on the x or y-axis to create a shape, then you find the volume of it... What are we, some engineers!?
This section of chapter seven is actually really cool and fun, it's cool to create the visual of what shapes we are making and figuring how we can find the volume of the shape we just made by using some random functions. This is a concept where we integrate all skills and knowledge we have already learned such as anti-deriving and integrating, but for some reason, things have been clicking for me! Maybe it was all the practice from trying to get my masteries done and learned, but this section has really been my favorite so far in AP CALC. I can start to feel myself really enjoy math again, maybe because I'm actually understanding what we are doing in class (lol).
There are two methods of finding the volume of the newly created shape. The DISK METHOD...
This section of chapter seven is actually really cool and fun, it's cool to create the visual of what shapes we are making and figuring how we can find the volume of the shape we just made by using some random functions. This is a concept where we integrate all skills and knowledge we have already learned such as anti-deriving and integrating, but for some reason, things have been clicking for me! Maybe it was all the practice from trying to get my masteries done and learned, but this section has really been my favorite so far in AP CALC. I can start to feel myself really enjoy math again, maybe because I'm actually understanding what we are doing in class (lol).
There are two methods of finding the volume of the newly created shape. The DISK METHOD...
And the WASHER METHOD...
Here is a video of an example of the disk method, which finds the volume of the shape with no hole, so the shape created is revolved around an aixs which is also a side of the shape.
Here is a video of an example of the washer method, which finds the volume of the shape with a hole, subtracting the top from the bottom.
Here is a video of an example of the washer method, which finds the volume of the shape with a hole, subtracting the top from the bottom.