Changing the function w.r.t in integration

In summary, "changing the function w.r.t in integration" involves finding the derivative of a function with respect to a variable in the context of integration, which allows us to solve for the original function. It is important in various fields of mathematics, physics, and engineering. This process is the inverse of regular differentiation and can be done using techniques such as the reverse power rule, integration by parts, and substitution. To improve skills in this area, one can practice with a variety of integration problems and use online resources.
  • #1
kartikwat
49
0
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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  • #2
It's not clear what you are asking. Can you provide an example of what you are trying to do?
 
  • #3
Do you mean, for example, [itex]\int x du[/itex] where [itex]u= x^2[/itex]? In that case [itex]du= d(x^2)= 2xdx[/itex] so the integral becomes [itex]\int x (2x dx)= 2\int x^2 dx[/itex].

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

Related to Changing the function w.r.t in integration

What is "changing the function w.r.t in integration"?

"Changing the function w.r.t in integration" refers to the process of finding the derivative of a function with respect to a particular variable in the context of integration. This allows us to solve for the original function, given its derivative.

Why is "changing the function w.r.t in integration" important?

Changing the function w.r.t in integration is important because it allows us to solve for the original function when given its derivative. This is useful in many areas of mathematics, physics, and engineering where finding the original function is necessary for further analysis.

How is "changing the function w.r.t in integration" different from regular differentiation?

The process of changing the function w.r.t in integration is essentially the inverse of regular differentiation. While differentiation involves finding the derivative of a function with respect to a variable, integration involves finding the original function when given its derivative with respect to a variable.

What are some common techniques for "changing the function w.r.t in integration"?

There are several techniques for changing the function w.r.t in integration, including the reverse power rule, integration by parts, and substitution. These techniques can be used to solve a wide range of integration problems involving changing the function w.r.t a variable.

How can I practice and improve my skills in "changing the function w.r.t in integration"?

The best way to practice and improve your skills in changing the function w.r.t in integration is to work on a variety of integration problems using different techniques. You can also use online resources, such as integration calculators and practice exercises, to test your understanding and identify areas for improvement.

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