How Does Changing Variables Affect Integrals in Calculus?

In summary, the conversation discusses the use of Jacobian determinants in integrals involving functions ##x = x(u,v)## and ##y = y(u,v)##, and the condition that the determinant must be non-zero. It also touches on the differentiation of ##x(u, v(u))## and the confusion surrounding it.
  • #1
LCSphysicist
646
161
Homework Statement
I am having a little trouble to see how the changes of variables works here.
Relevant Equations
Functionals.
Be ##x = x(u,v) y = y(u,v)##, if ##F = \int f(x,y,y')dx## and the Jacobian's determinant different of zero, ##v = v(u)##
##{\Large {J = \int F[x,y,y']dx ---> \int F[x(u,v),y(u,v),\frac{y_{u} + y_{v}v'}{x_{u} + x_{v}v'}](x_{u} + x_{v}v')du}}##

The last term in the bracket is confusing me, how to get it?
 
Physics news on Phys.org
  • #2
You have ##x = x(u, v(u))## and you need ##\frac{dx}{du}##. Can you do that differentiation?
 
  • Like
Likes LCSphysicist
  • #3
PeroK said:
You have ##x = x(u, v(u))## and you need ##\frac{dx}{du}##. Can you do that differentiation?
Oh, so we can do y' = dy/dx = dy/du/dx/du, i was confusing terms, but now it is ok, thx
 
  • Like
Likes PeroK

Related to How Does Changing Variables Affect Integrals in Calculus?

What is the definition of changing functional variables?

Changing functional variables refers to the process of altering the independent variable in an experiment or study to observe its effect on the dependent variable. This allows researchers to determine the relationship between the two variables.

Why is changing functional variables important in scientific research?

Changing functional variables is important because it allows scientists to test hypotheses and make conclusions about cause and effect relationships. It also helps to control for other variables that may influence the outcome of the experiment.

What are some common examples of changing functional variables in experiments?

Some common examples of changing functional variables include altering the dosage of a medication, changing the temperature or pH in a chemical reaction, or adjusting the amount of light exposure in a plant growth experiment.

How do scientists determine the appropriate values for changing functional variables?

Scientists determine the appropriate values for changing functional variables through careful planning and consideration of previous research. They may also use statistical analysis to determine the most effective range of values to test.

What are some potential limitations of changing functional variables in experiments?

Some potential limitations of changing functional variables include the possibility of confounding variables, which may influence the results of the experiment. Additionally, ethical considerations may limit the range of values that can be tested in certain experiments.

Similar threads

  • Calculus and Beyond Homework Help
Replies
21
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
727
  • Calculus and Beyond Homework Help
Replies
2
Views
531
  • Calculus and Beyond Homework Help
Replies
3
Views
691
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
372
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
960
  • Calculus and Beyond Homework Help
Replies
16
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
803
Back
Top