# pappus

1. ### theorem of pappus

hello the question i need help with goes as follows. sketch the solid region contained within the sphere, x^2+y^2+z^2=16, and outside the cone, z=4-(x^2+y^2)^0.5. b) clearly identifying the limits of integration, (using spherical coordinates) set up the iterated triple integral which would...
2. ### pappus

I have now sorted the first part of this question but cant get anywhere with part(b): 3) given area of ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 is \pi ab and that the volume generated when this area rotates through \pi about the x-axis is \frac{4}{3}\pi ab^2 use pappus' theorem to find...
3. ### reduction,centroid,pappus

1) question asks to find reduction formual for I_(n)=\int \frac{sin(2nx)}{sin(x)} then it asks hence or otherwise find: \int_0^{\frac{\pi}{2}} \frac{sin(5x)}{sin(x)} only way i can do this is to do a reduction formula for \int_0^{\frac{\pi}{2}} \frac{sin(nx)}{sin(x)}...
4. ### Pappus's Theorem and Some Integrals

Hey guys, I was wondering if it would be possible for someone to check my work on a few calculus problems and, if they're wrong, to tell me what I'm doing wrong. Thank you very much in advance. Problem 1. R is the region bounded by y = sinx and the lines x = 0 and x = \frac{\pi}{2}. a...
5. ### Pappus theorem

I have been given the curve y= ((x)^0.5)/4 It is bounded by the line y=0 and x=1. and rotated around the x-axis. I found the volume to be pi/32 using pi x intergral y^2 I have then been asked to check the volume using pappus theorem, but i don't know how to do that. Please Help! :confused:
6. ### Triple Integration with spherical coordinates and Pappus centroid theory

Hello, Uncertain about an homework textbook question. It reads: Part A: Sketch the solid region contained within the sphere x^2 + y^2 + z^2 = 16, and outside of the cone, z = 4 - sqrt(x^2 + y^2). Does anybody know of a free 3D graphing program/calculator online. I can kind of picture...