Integrating Functions with Only One Variable: A Guide for Beginners

In summary, the student is seeking help with integrating a function where y is the only variable and x and w are constants. They are familiar with different methods of integration such as substitution, trigonometric substitution, by parts, and partial fraction decomposition. The student is unsure of where to begin and asks for guidance. The advice given is to try out the different methods and not to be discouraged by potential wasted effort and paper as it is a part of the learning process.
  • #1
NihalRi
134
12
1. Homework Statement
image.jpg

I'm trying to integrate this, the only variable is y the others(x,w) are all constants.

Homework Equations


The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.

The Attempt at a Solution


Looking at this I can't think of where I'd begin, should I rearange? Is it multistep? It it possible ? I'd appreciate any help :)
 
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  • #2
NihalRi said:
1. Homework Statement
View attachment 108595
I'm trying to integrate this, the only variable is y the others(x,w) are all constants.

Homework Equations


The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.

The Attempt at a Solution


Looking at this I can't think of where I'd begin, should I rearange? Is it multistep? It it possible ? I'd appreciate any help :)

PF rules say that you are required to put in effort and show your work. So, try out the methods you have learned. If Method I does not work, then try Method II. If that does not work, turn to Method III, etc. And yes, indeed, it takes some (possibly wasted) work and uses a lot of (possibly wasted) paper but that is how you will learn.
 
Last edited:

What is "integrating this function"?

Integrating a function is the process of finding the function that, when differentiated, gives the original function. It is essentially the reverse process of differentiation.

Why is integrating a function important in science?

Integrating a function is important because it allows scientists to calculate important quantities such as area, volume, and displacement, which are crucial in many scientific applications. It also helps in solving differential equations, which are used to model many natural phenomena.

What are the different methods of integrating a function?

There are various methods for integrating a function, such as the power rule, substitution, integration by parts, and partial fractions. The choice of method depends on the form of the function being integrated.

What is the notation used for integrating a function?

The notation used for integrating a function is the integral sign (∫) followed by the function to be integrated and then the variable of integration. For example, the integral of f(x) with respect to x would be written as ∫f(x)dx.

How can one check if the integrated function is correct?

One can check the integrated function by differentiating it and comparing it to the original function. If the result is the same, then the integrated function is correct.

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