Integral Bounds Determination in Spherical Coordinates

DHB_Integral
Messages
3
Reaction score
0

Homework Statement



How to determine the integral bounds of phi in spherical polar coordinates. Please see my exact question at the end of page 2 of 2 in attachments.

Homework Equations



Please see my attachments

The Attempt at a Solution


Please see my attachments.
 

Attachments

  • I_Page_1.jpg
    I_Page_1.jpg
    24 KB · Views: 582
  • I_Page_2.jpg
    I_Page_2.jpg
    30.9 KB · Views: 542
Last edited:
Physics news on Phys.org
I just tried out the integral bounds of phi , it can work getting the correct result. but It cannot convince myself in terms of the bounds of phi, based on the graph on page 1, it should be equal to pi/4. So, how to prove the bounds of phi? Please help with question.

Thanks a lot in advance.
 
Last edited:

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Triple Integral To Find Volume Between Cylinder And Sphere
Replies
2
Views
2K
How to calculate a sink using spherical coordinates
Replies
7
Views
1K
Center of mass of spherical shell inside of cone (Apostol Problem).
Replies
3
Views
2K
When to use the Jacobian in spherical coordinates?
Replies
2
Views
3K
Obtaining the moment of inertia of a sphere and spherical shell
Replies
6
Views
982
How to set bounds in cylindrical coordinates analytically?
Replies
4
Views
1K
Verifying the flux transport theorem
Replies
4
Views
2K
Understanding Integration Limits for Spherical and Cartesian Coordinates
Replies
1
Views
2K
Problem integrating with the disk method
Replies
5
Views
1K
Interpret Riemann sum to determine integral
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top