volumes: rotating around y=x etc. (1 Viewer)

[blackfriday]

what is the best way to rotate a function around a line, like y=x or something similar?

i say take a slice perpendicular to the line you are rotating around, lum says you split it up and force it into something you can rotate around the x- or y-axis.

thanks.

 

[justchillin]

what is the best way to rotate a function around a line, like y=x or something similar?

i say take a slice perpendicular to the line you are rotating around, lum says you split it up and force it into something you can rotate around the x- or y-axis.

thanks.

The whole thing about slicing and cylinderal shells is to take the slice perpendicular to the axis through which you are roating. So split the areas up into different parts...

 

[blackfriday]

dont quite getcha there...um take for example x² + y² = 16 around y=x. what i would do is find perpendicular distance from any point (x,y) to the line y=x and treat that as my slice, and my limits would be 0 and 4. is that the way to do it?

 

[thunderdax]

dont quite getcha there...um take for example x² + y² = 16 around y=x. what i would do is find perpendicular distance from any point (x,y) to the line y=x and treat that as my slice, and my limits would be 0 and 4. is that the way to do it?

I'd hate to be pedantic, but with that question I'd just say the area is equal to a sphere and work from there. But, I think I'd just rotate the x and y axes (if you know what I mean) to X and Y, and use those references. I don't think we'll get a question like that.

 

[blackfriday]

you know what? i bloody well hope you're right we dont get something like that.

 

[Stefano]

you know what? i bloody well hope you're right we dont get something like that.

Ditto.

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Please get rid of that [censored]!

 

[DRAGONZ]

They *CAN* be really nasty and give you one of those questions, but I've never been bothered to learn about how to do it properly.

If you have the Cambridge textbook, go look at the question on the bottom of page 183 and the solution on page 184 ...