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Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

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Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x - axis.

 

asked Feb 12, 2015 in CALCULUS by anonymous
reshown Feb 12, 2015 by goushi

1 Answer

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Step 1:

The equations are image and image.

The volume of the solid generated revolving about the - axis.

Washer method:

The outer radius of revolution is image.

The inner radius of revolution is image.

Substitute image and in .

image

image

Integrate between 0 and 1.

image

image

Step 2:

Solve the integral by using substitution method.

image

Apply derivative on each side with respect to image.

image

image

image

Substitute image and image in image.

image

image

Apply formula image.

image

Back substitute image.

image

image

image

image

image

image.

The volume of solid is image cubic units.

Solution:

The volume of solid is image cubic units.

 

answered Feb 21, 2015 by casacop Expert

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