i just dont understand these problems:
1. region bounded by graph of f(x)=cosx and the x-axis, x E [-pi/2, pi/2], is revolved about the x-axis. find the volume of the resulting solid.
2. region bounded by the y-axis and the graphs of y=sinx and y=cosx, 0
TIA
2006-09-16 14:18:00 · 2 answers · asked by DoughboyFresh 2 in Science & Mathematics ➔ Mathematics
Pappus's centroid theorem The second theorem states that the volume V of a solid of revolution generated by rotating a plane figure F about an external axis is equal to the product of the area A of F and the distance d2 traveled by its geometric centroid
1) We know that the area is symmetric according to axis y. Therefore the x coordinate of the centroid is 0. We have to calculate the y coordinate of centroid:
The height of centroid is pi/16.
The revolving area is 2.
The volume is 2*pi/16*pi*2=pi^2/4
2) The height of centroid is (2^0.5+1)/8
The area is 2^0.5-1
The volume is 2(2^0.5+1)*pi*(2^0.5-1)/8=pi/4
2006-09-16 15:05:57 · answer #1 · answered by Farshad 2 · 0⤊ 0⤋
It sounds like you have problems with Calculus in general. Surely there is some tutoring help at your school It would be much better to work directly with someone. For example, it would be better to draw some 3-D pictures to start with so you can visualize the problem.
2006-09-16 21:48:41 · answer #2 · answered by DadOnline 6 · 0⤊ 0⤋