Spherical coordinates triple integral

[brad sue]

Hi,

Please can someone help me with this problem:

find the triple integral over T( using spherical coordinate)

T: 0<=x<=1
0<= y<=sqrt(1-x^2)
sqrt(x^2+y^2)<= z <= sqrt(2-(X^2+y^2))

please help me just to find the boundaries of the integrals.
I tried but I did not find the solution of the textbook. ( because I set the wrong triple integral) I also tried to draw a picture but ...nothing


Thank you

 

[da_willem]

Use the relations between Cartesian (x,y,z) and spherical coordinates ([itex]r,\theta,\phi[/tex]) to substitute for x, y and z:

$$x=rsin(\phi)cos(\theta)$$
$$y=rsin(\phi)sin(\theta)$$
$$z=rcos(\phi)$$

where phi is the angle between a vector and the z-axis. theta is the angle between the projection on the x,y plane ad the x-axis.

 

[TD]

Also don't forget your Jacobian, in this case being r²sin(phi).