Solve Double Integral: ln(u) du

In summary, the conversation is about solving a double integral involving ln(u) and the confusion over the correct notation and method for solving it. One person suggests using integration by parts and clarifies the notation for ln(u) and u. The other person confirms their understanding and suggests a different notation for the integral. The conversation ends with a summary of the solution using substitution and integration by parts.
  • #1
KSCphysics
31
0
One of my recent problems is with double integrals... and I am having a brain fart on the [tex]\int ln(u) du [/tex] can you do this?
 
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  • #2
You can do it by parts. Consider that
[tex]\frac{d}{dx} x \ln x = \ln x + 1[/tex]
 
  • #3
hrmm... i see what your saying..
 
  • #4
wouldn't it just be 1/u?
unless that little dash is a negative sign mean your are integrating 1/ln(u) then I'm not sure but i think it would just be u then, but i am probably wrong
 
  • #5
iluvsr20s,

You are probably confused with the fact that [tex]\int \frac{1}{u} du = \ln x + c[/tex]. It is not the other way around.
 
  • #6
Pfft...

... hehe. this ain't too bad. Can we change it to int(ln(x),dx) though? It's how I've always done it notation-wise.

let u = ln(x), dv = dx --> du = 1/x(dx), v = x

So, u*v -int(v,du) = int(u,dv)

x*ln(x) - int(1,dx) = int(ln(x),dx)
x*ln(x) - x = int(ln(x),dx)

Et voila.
 

1. What is a double integral?

A double integral is a type of mathematical operation that involves solving for the area under a two-dimensional curve. It is similar to a regular integral, but it involves finding the volume under a surface rather than the area under a curve.

2. What is the process for solving a double integral?

The process for solving a double integral involves evaluating the inner integral first, then using the resulting value as the upper limit for the outer integral. This process is repeated until all integrals have been evaluated.

3. How do you solve a double integral with natural logarithms?

To solve a double integral with natural logarithms, the first step is to convert the integral into its equivalent form using the properties of logarithms. Then, the inner integral can be evaluated using integration by parts, and the resulting value can be used in the outer integral.

4. Can a double integral with natural logarithms have multiple solutions?

No, a double integral with natural logarithms can only have one unique solution. However, there may be different methods or approaches to solving the integral that can yield slightly different results.

5. What are some real-life applications of solving double integrals with natural logarithms?

Double integrals with natural logarithms have many applications in physics, engineering, and economics. For example, they can be used to calculate the center of mass of an object, the electric potential of a charged particle, or the expected return on an investment.

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