Ace W.

asked • 10/08/19

Calculating Volume Of a Region via Washer

Calculate the volume obtained by rotating the region in the first quadrant bounded by x2+y2=0, y=x, and x=0.

I understand how to use shell method with this question (radius: x, height: (1-x2)1/2-x, bounds: 0 to sqrt2/2), with the answer being 2∏/3-∏sqrt2/3. How would you calculate this using washer/disk method however? I tried using bounds [0,sqrt2], but I don't come out with the correct answer.


Another side note, when do you use dy versus dx. I understand dx is taking vertical slices and dy is taking horizontal slices perpendicular to the y axis?


Thank you!

Doug C.

Check your question for accuracy. X^2 + y^2 = 0? Revolve about what line?
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10/08/19

Ace W.

About the y-axis sorry!
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10/08/19

William W.

x^2 + y^2 = 0 is a point at the origin. There's nothing to rotate.
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10/08/19

Doug C.

You sure it is not x^2+y^2 = 1? That would make sense for the answer you supplied in your question.
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10/08/19

Ace W.

Yes, it was x^2+y^2=1. Typo sorry.
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10/08/19

Doug C.

Ok, video answer on the way for how to evaluate using disk method.
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10/08/19

Ace W.

Thank you so much! 😊
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10/08/19

1 Expert Answer

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Doug C. answered • 10/08/19

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Doug C.

If you want to visit the Desmos graph used for the diagram and calculations attach /calculator/mjbjsx17yc to the URL for desmos.
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10/08/19

Ace W.

Oh! Thank you so much! I had tried to set it up so that it was integral from 0 to sqrt 2 for integrand ((1-x)^(1/2))^2 -x^2. It makes sense now :).
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10/08/19

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