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Applications of the Integral

Applications of the Integral. Volumes of Revolution. Example (1) Find the volume v resulting from the revolution of the region bounded by: y=√x frm x=0 to x=1 about the x-axis.

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Applications of the Integral

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  1. Applications of the Integral

  2. Volumes of Revolution

  3. Example (1)Find the volume v resulting from the revolution of the region bounded by:y=√x frm x=0 to x=1 about the x-axis.

  4. Example (2)Find the volume v resulting from the revolution of the region bounded by:y=√(a2-x2 ) from x=-a to x=a and the x-axis about the x-axis.

  5. Example (2)*Find the volume v of a sphere of radius a:Method: Find volume of revolution of the region bounded by the upper half of the circle x2+y2=a2 and the x-axis about the x-axis. That’s the area bounded by:y=√(a2-x2 ) from x=-a to x=a and the x-axis about the x-axis.

  6. Example (3)Find the volume v resulting from the revolution of the region bounded by:y=x2, y=x about the x-axis.

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