Question

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?

Answer 1

Step 1:

The curve equations are and .

Definition of volume:

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

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

Step 2:

Outer radius is .

Inner radius is .

Integrate the region between .

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

Solution:

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