I'm pretty new to discs/shells and I'm having a hard time with it. Here's a problem I've been stuck on for a few days now:(adsbygoogle = window.adsbygoogle || []).push({});

I need to find the volume of a solid by revolving the region bounded on the left by x = y^2 +1 and by x = 5 on the right side. It is revolved around x = 6.

My work (I can't figure out how to make it appear as it would in the book, so I apologize if this becomes confusing):

I took the integral from -2 to 2 of (pi) times (6 - (y^2 +1))^2.

int from -2 to 2 ((pi) (5-y^2)^2) dy

(pi) int from -2 to 2(25 - 10 y^2 + y^4) dy

(pi) ((25y - (10y^3/3) + (y^5/5) from -2 to 2)

(pi) ((50 - (80/3) + (32/5)) - (-50 + (80/3) - 32/5))

(pi) (100 - (160/3) + (64/5))

(pi) ((1500/15) - (800/15) + (192/15))

= 892(pi)/15

I tried using the shell method but that turned out even worse, so I figure I'm supposed to use the disc method.

Any help or tips?

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# Homework Help: Disc/Shell Problem

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