Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

find the volume of the solid formed by revolving the region bounded by y=x^2, y=0, and x=2 about the y axis

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
Do you know about multivariable calculus perhaps? Or do you want the easy-not-understanding-what-you're-doing way
The answer is 8pi
No, I am supposed to use the Disk Washer method. I can do it with antiderive(2-y) to get the right answer but I'm pretty sure that's not following th formula I'm given which is outer radius minus inner radius.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Disk Washer?
There's a hole in the solid.. so it's called Washer Method.
So how does this method work?
I do antiderivative from a-b in terms of x or y (y in this case because I rotate about y axis) pi (outer radius)^2 - (inner radius)^2
\[\int\limits_{a}^{b} \pi (outer radius)^2 -(innerradius)^2 dx\]
I don't how that works, I'm afraid.
|dw:1359838432884:dw|
|dw:1359838561883:dw|So let's look at one slice.
Oh you're doing the washer/disk method, my mistake.. Lemme slice that differently.
|dw:1359838731527:dw|Ok this type of slice will give us a Disk.
|dw:1359838764034:dw|So we want to get the Volume of this disk.
The outer radius appears to be the line x=2. And the inner radius our function which is in terms of x, we'll need it in terms of y to integrate since we sliced in the y direction (dy thickness)
\[\large y=x^2 \qquad \rightarrow \qquad x=\sqrt y\]
\[\large V=\pi\left[(2)^2-(\sqrt y)^2\right]dy\]
Then to find the total volume in this enclosed area, we Integrate (add up all the slices) from one intersecting point to another. Where do they intersect? Ummm looks like.. y=0 and y=4?
Simplifying things down gives us, \[\large \pi \int\limits_0^4 4-y \;dy\]
Imma check my work real quick to make sure I didn't make a mistake somewhere. A little tired, it's possible. lol
Yah I think that's right. Confused about any of that? I went through it a little sloppy D:
It's right. I realize what I did wrong! I had the wrong intersections/points. I did instead from -2 to 2.. not realizing that it was based on terms of y . thank you so much!
Oh cool c:

Not the answer you are looking for?

Search for more explanations.

Ask your own question