- #1
amiras
- 65
- 0
Homework Statement
Evaluate triple integral
z^2 dxdydz
throughout
i) the part of the sphere x^2 + y^2 + z^2 = a^2 (first octant)
ii)the complete interior of the sphere x^2 + y^2 + z^2 = a^2 (first octant)
Homework Equations
It is probably good idea to work in spherical coords.
z = r*cosφ
x = r*sinφ cosθ
y = r*sinφ sinθ
dxdydz = r^2 sinφ drdφdθ
The Attempt at a Solution
I'l start at part ii) because its the part I can do.
Here the boundaries are:
0 =< r < a
0 =< φ < pi/2
0 =< θ < pi/2
the integration now becomes:
(Int[r=0, a] r^4 dr )( Int[φ=0, pi/2] sinφcos^2 φ)( Int [θ=0, pi/2]) = r^5/30 * pi
i) But for part i), I am confused. The integral should be evaluated only on the surface of the sphere. The radius a is constant in length, so how should r be defined?
a < r < a, makes no sense.
Need advice.
Last edited: