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Suppose we are calculating moment of inertia of a uniform rod with linear density $\lambda$ and length $L$.Now the total moment of inertia of the rod is $\frac{ML^2}{12}$ which we find by integrating.Now the total moment of inertia must be the area under some curve as the definition of integral is the area under the curve.My question is what is that curve(I mean the function and the independent variable)?Could you please show the graph?Also should we think of integrals as area under the curve always or continuos sums?

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  • $\begingroup$ See the first example here $\endgroup$ – user10354138 Feb 23 at 7:16
  • $\begingroup$ I am sorry,but how does that answer my question?I asked for the curve and graph $\endgroup$ – Aritra Barua Feb 23 at 7:31
  • $\begingroup$ You can't graph $x\mapsto x^2$? $\endgroup$ – user10354138 Feb 23 at 7:33
  • $\begingroup$ Why is that function f(x)=x^2?Could you please show me the graph of the moment of inertia and validate the x^2 function? $\endgroup$ – Aritra Barua Feb 23 at 7:47
  • $\begingroup$ Moment of inertia about an axis $\ell$ is defined as the integral $I(\ell)=\int\operatorname{distance}(\mathbf{x},\ell)^2\,\mathrm{d}m(\mathbf{x})$. $\endgroup$ – user10354138 Feb 23 at 7:50

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