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Dear Abe,

I'm learning for my Calculus exam, but this exercise isn't very clear to me:

y=(x-2)^3

y=x-2

The formula for the volume is V=pi(integral |f(x)|²dx

The correct result is 8pi/21

Would be delighted if you'd help me out with this exercise.

Regards,

Bob

Hello Bob,

The two curves intersect at x=1, 2, and 3 (see attached graph).

However, it is not necessary to break the problem into two separate

integrals, since from x=1 to 2 and x=2 to 3, the outer radius of the

solid formed (by rotating about the x-axis) are both y-x-2 with y-(x-2)^3

being the inner radius. Hence, one integral can take care of the entire

volume! he integral also appears in the attached image (as wellas the

answer of 8pi/21.

I hope this helps.

Abe

Calculus

Answers by Expert:

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Over 15 years teaching at the college level.**Organizations**

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.**Education/Credentials**

B.S. in Mathematics from Rensselaer Polytechnic Institute

M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook