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Definite integrals, areas and volumes

Definite integrals, areas and volumes · Diagrams

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Strips rotate into washers about either axis

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For ordered nonnegative radii, a vertical strip rotates about the x-axis into a washer of thickness delta x; a horizontal strip rotates about the y-axis into a washer of thickness delta y. Each area is pi times outer-radius squared minus inner-radius squared.
For ordered nonnegative radii, a vertical strip rotates about the x-axis into a washer of thickness delta x; a horizontal strip rotates about the y-axis into a washer of thickness delta y. Each area is pi times outer-radius squared minus inner-radius squared.
For ordered nonnegative radii, a vertical strip rotates about the x-axis into a washer of thickness delta x; a horizontal strip rotates about the y-axis into a washer of thickness delta y. Each area is pi times outer-radius squared minus inner-radius squared.
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