/sci/ - Science & Math

Difference between the shell method washer method

Okay so for both of them I find the points of intergration by getting x. Is there a difference in how I do this. My professor in shell example sets the functions equal to each other and then factors x.
y=x^2, y^2=8x

For the washer method he solves for x,
y=x^2, y=4-x^2

But its only different because the y values are different, if you switched the sets of y values from the washer to dish you would still find the points of intergration the same way right?


And then for the formula for washers its the antiderivative of
pi * [(r1^2)-(r^2^2)
?

And for shell method its antiderivative of
2pix * (r1-r1)
So instead of squaring r1 and r2 I multiply them by x, and its always just x right that doesn't change; its never like x^2 or 2x?

And then after that I just solve

Is all that the proper method?
I still don't really get what determines whether its r1 or r2

And when is says about the y axis or about the x axis what does that mean?, what changes in the formula

Difference between the shell method washer method

Okay so for both of them I find the points of intergration by getting x. Is there a difference in how I do this. My professor in shell example sets the functions equal to each other and then factors x.
y=x^2, y^2=8x

For the washer method he solves for x,
y=x^2, y=4-x^2

But its only different because the y values are different, if you switched the sets of y values from the washer to dish you would still find the points of intergration the same way right?


And then for the formula for washers its the antiderivative of
pi * [(r1^2)-(r^2^2)
?

And for shell method its antiderivative of
2pix * (r1-r1)
So instead of squaring r1 and r2 I multiply them by x, and its always just x right that doesn't change; its never like x^2 or 2x?

And then after that I just solve

Is all that the proper method?
I still don't really get what determines whether its r1 or r2

And when is says about the y axis or about the x axis what does that mean?, what changes in the formula