Tuesday, 23 May 2017

integration - How to solve the given integral?



I have the following integral, which is part of a larger function, but this is the only part I'm not sure about how to solve:



(xda(x)dx)dx




The variable a (depending on x) is derived over x, and this derivative is multiplied with x. I want to integrate the entire thing over x. An online integral calculator suggested the result was zero, but I am uncertain as to whether I defined the equation properly in that page.



Could you help me solving this integral?


Answer



We have that ddxa(x)=a(x). Thus, we get, I=xa(x)dx =xa(x)dx(a(x)dx)ddx(x)dx =xa(x)a(x)dx0



We have calculated the integral using integration by parts where u=x and dv=a(x)dx. Hope it helps.


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