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Mass of the wire of a curve described by $$y = x^2 +1 $$ where $0\le x\le 1$ with density $$ \rho(x,y) = 12x $$

I couldn't get the correct answer for this one.

What I did:

$$ m = \int^{0}_{1}\int^{1}_{x^2} 12 x dy dx $$

that gives me $3$, which is not correct.

  • 3
    Did you look at http://math.stackexchange.com/questions/77486/wire-mass-line-integral?rq=1 at all?2012-11-03
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    Should it not be $\int_0^1 12 x (x^2+1) dx = \int_0^1 \int_0^{x^2+1} 12 x \, dy \, dx$?2012-11-03
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    Is it because it is a "Wire" so you cannot integrate it the way I did above and have to use Line integral?2012-11-03
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    Also, I'm not sure if copper.hat's method is valid or not. Can anyone confirm?2012-11-03
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    @40Plot: Have you read the post that David Wallace linked to? It describes exactly how to do these kinds of problems. Yes, you have to use a line integral rather than integrating over a 2D region.2012-11-03
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    The density is a linear density?2012-11-03

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