Changing the function w.r.t in integration

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SUMMARY

This discussion focuses on changing the function with respect to integration, specifically addressing the integral of a function other than x. The example provided illustrates the process of integrating \(\int x \, du\) where \(u = x^2\), leading to the transformation of the integral into \(\int x (2x \, dx) = 2\int x^2 \, dx\). The general rule highlighted is that \(\int f(x) \, dg(x) = \int f(x) \, g'(x) \, dx\), emphasizing the relationship between the differential and the function being integrated.

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kartikwat
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How to change the function w.r.t we are doing integration(function other then x) .what does it mean to do so.
 
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It's not clear what you are asking. Can you provide an example of what you are trying to do?
 
Do you mean, for example, \int x du where u= x^2? In that case du= d(x^2)= 2xdx so the integral becomes \int x (2x dx)= 2\int x^2 dx.

In general, \int f(x) dg(x)= \int f(x) g'(x)dx because dg(x)= g'(x)dx.
 

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