How do you do this weird integral?

In summary, the integral is an equation that asks for the amount of a function at a given point in space, and it can be solved by integrating by parts or by using an equation that relates the function to the independent variable. There are many cases that could apply depending on the function being solved for.
  • #1
somethingstra
17
0
Hello,

I came upon this strange integral:

[tex]\int \frac{f(x,y)}{x}dx[/tex]

How would one attempt to solve this? Would integration by parts do?
 
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  • #2
What is f(x,y) ? Unless you have a more specific formula, there is not much you can do to compute or simplify the integral.
 
  • #3
Like yyat said, unless we have more info about f(x,y) we can't really say anything about it.
 
  • #4
Are yoiu going to tell us what f(x,y) is?
 
  • #5
If x and y are independent variables, then just integrate normally with respect to x and treat y as a constant.

If y = g(x), then plug in.

If y is an implict function of x, some method of integration might make your life easier. This would be a lot easier to do on a case by case basis.
 
  • #6
or if: f(x,y)=0 the integral is zero(0) or if

f(x,y)=1=> integral is ln|x|

(just messing around)!
 
  • #7
... just for clarification, I was being serious. I think I just about listed all the cases. Did I miss one?
 
  • #8
csprof2000 said:
... just for clarification, I was being serious. I think I just about listed all the cases. Did I miss one?

Excuse post #6. If you interpreted it as a joke to your post, it was not meant to be so.

I think you mentioned about all possible cases. The OP, might also consider differetiating under the integral sign as well, if applicable. But since there are no info whatsoever about the nature of f(x,y), then god help us.
 
  • #9
No offense taken!

I agree that the problem is sort of vague. I mean, I could ask you how you solve the equation

f(x) = 0.

It... uh... sort of depends on, well, what f(x) is.
 
  • #10
Well, I meant f(x,y) to just be an arbitrary function of x and y. My question was meant to find out what the general form of the integral would be. Sorry for the confusion!
 

1. How do you approach solving a complicated integral?

The first step in solving a complicated integral is to identify the type of integral it is, such as a definite or indefinite integral, and the techniques that can be used to solve it. Then, break down the integral into smaller, more manageable parts and apply appropriate integration techniques to each part.

2. What are some common strategies for solving difficult integrals?

Some common strategies for solving difficult integrals include using substitution, integration by parts, partial fractions, and trigonometric identities. Another helpful strategy is to simplify the integrand using algebraic manipulation or simplification rules.

3. What do you do when you encounter an integrand with no obvious solution?

In cases where there is no obvious solution to an integrand, it is important to try different techniques and see which one works best. It may also be helpful to consult integration tables or software to check for any patterns or special cases that can be applied.

4. How can you check if your solution to an integral is correct?

One way to check if your solution to an integral is correct is to differentiate the result and see if it matches the original integrand. Another method is to use integration tables or software to verify the solution.

5. What are some tips for mastering integration?

To master integration, it is important to have a strong understanding of basic algebra and calculus concepts. Practice solving a variety of integrals using different techniques and seek help from textbooks, online resources, or a tutor if needed. It is also helpful to review and understand the steps involved in solving each type of integral.

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