How do I set up a triple integral using cylindrical coordinates?

-EquinoX-
Messages
561
Reaction score
1

Homework Statement



http://img3.imageshack.us/img3/7558/47586628.th.jpg

Homework Equations





The Attempt at a Solution



I am quite confused whether I should use cartesian, cylindrical, and spherical coordinate.. how do I approach this problem
 
Last edited by a moderator:
Physics news on Phys.org
Use cylindrical coordinates. Hint: Integrate the function z=r over a suitable range of r and theta (this will be a double integral).
 

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

Cylindrical Coordinates Triple Integral -- stuck in one place
Replies
1
Views
2K
The volume of a "spherical cap" using triple integrals
Replies
9
Views
1K
Triple integral in cylindrical coordinates
Replies
2
Views
2K
Center of Mass Using Triple Integrals Question
Replies
4
Views
3K
Is the Triple Integral in Cylindrical Coordinates Correctly Solved?
Replies
12
Views
2K
Bounded regions and triple integrals
Replies
6
Views
2K
Change integration limits for cylindrical to cartesian coord
Replies
1
Views
1K
Volume of ice cream cone triple integral
Replies
6
Views
3K
How to set bounds in cylindrical coordinates analytically?
Replies
4
Views
1K
Spherical and Cylindrical Triple Integral Conversion: Homework Problem
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top