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Let R be the region bounded by y=x^2, and y=5x-6. Find the volume of R rotated about the x-axis.?

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Let R be the region bounded by y=x^2, and y=5x-6. Find the volume of R rotated about the x-axis.?

I already did the problem for a quiz, and the answers just did not seem right at all. I got x=6 and x=-1 for the initial x values, and that sounds horribly wrong since the lines don't intersect there. can you help?
asked Feb 14, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The curve equations are image and image.

Definition of volume:

The volume of the solid  is image, where image is the cross sectional area of the solid , where

image

To find the point of intersection, equate the above equations image and image.

image

Step 2:

Outer radius is image.

Inner radius is .

Integrate the region between image.

image

The volume of region bounded by the curves is image cubic units.

Solution:

The volume of region bounded by the curves is image cubic units.

answered Feb 24, 2015 by Lucy Mentor
reshown Feb 24, 2015 by casacop

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