How to Correctly Use Substitution for Polar Coordinates in Integrals?

In summary, "change to polar" is a mathematical operation used to convert rectangular coordinates to polar coordinates. This can be done using formulas for distance and angle. It is useful for simplifying calculations and graphing certain functions, but may not be suitable for all situations. Polar coordinates can also be converted back to rectangular coordinates using specific formulas. It is important to understand their limitations when using them.
  • #1
Qyzren
44
0
http://img187.imageshack.us/my.php?image=polargy3.jpg



The Attempt at a Solution


http://img484.imageshack.us/my.php?image=picture155jy1.jpg
i get an extra cos² thi term! WHY!
am i doing the substitution completely wrong?? or i forgot/left something out which i can not seem to see!

Thank you
 
Physics news on Phys.org
  • #2
4th line, [itex]dw_1= -w\sin \phi d\phi[/itex] unfortunately :(
 
  • #3
oops, i meant to write dw1 = cos thi dw.
nevermind, i got it.
I have to use Jacobian matrix instead of what i did.
 
Last edited:

FAQ: How to Correctly Use Substitution for Polar Coordinates in Integrals?

What is "change to polar"?

"Change to polar" is a mathematical operation that converts coordinates in a rectangular coordinate system to polar coordinates. It is often used in physics, engineering, and mathematics to simplify calculations and solve problems.

How do I change coordinates to polar?

To change coordinates to polar, you can use the following formulas:

r = √(x^2 + y^2) where r is the distance from the origin and x and y are the rectangular coordinates

θ = tan^-1 (y/x) where θ is the angle from the positive x-axis to the point

Why would I need to change to polar coordinates?

Changing to polar coordinates can be useful in situations where calculations involving angles and distance are easier to solve than using rectangular coordinates. It is also helpful in graphing certain functions, such as circles and spirals.

Can I change polar coordinates back to rectangular coordinates?

Yes, you can convert polar coordinates back to rectangular coordinates using the following formulas:

x = r cos(θ) where x is the horizontal coordinate and θ is the angle in radians

y = r sin(θ) where y is the vertical coordinate and θ is the angle in radians

Are there any limitations to using polar coordinates?

Polar coordinates are not suitable for all situations, especially when working with complex shapes or calculations involving multiple variables. It is important to understand when and how to use polar coordinates effectively and to be aware of their limitations.

Similar threads

Integration of acceleration in polar coordinates
Replies
24
Views
2K
Change of Variables: Integrals w/Polar Coordinates
Replies
2
Views
1K
Double Integration in Polar Coordinates
Replies
3
Views
1K
What are the correct ways to use polar form in solving integrals?
Replies
1
Views
2K
Trying to use polar coordinates to find the distance between two points
Replies
7
Views
2K
Double Integrals (polar coordinate)
Replies
1
Views
1K
Trying to find this double integral using polar coordinates
Replies
14
Views
3K
Region bounded by a line and a parabola (polar coordinates)
Replies
22
Views
2K
Double integral on triangle using polar coordinates
Replies
3
Views
2K
Evaluating Cartesian integral in polar coordinates
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top