Evaluate the triple integral (with spherical coordinates)

[melihaltintas]

Homework Statement

Firstly sorry for my bad english,i have a one question for you(İ try it but i didn't solve it )

Homework Equations

The Attempt at a Solution

i know problem will be solved spherical coordinates but i don't know how i get angles (interval) theta and fi ?
\int_{0}^{\infty}\int_{0}^{\infty}\int_{0}^{\infty}e^{-\sqrt{x^2+y^2+z^2}}\,dxdydz

Mod note: Fixed LaTeX. Read what tiny-tim said below.[/color]

 

[HallsofIvy]

You get the angles by thinking about what the spherical coordinate variables mean. \phi is the angle from the positive z-axis to the negative x-axis and, to cover all space, would normally go from 0 to \pi. Since you want z to stay positive, you want \phi to go from 0 to \pi/2. \theta goes around a complete circle in the xy-plane in going from 0 to 2\pi. Since the first quadrant is 1/4 of that, \theta goes from 0 to \pi/2. Finally, there is no upper limit on the distance from the origin to any point in the first octant so \rho goes from 0 to \infty.

 

[tiny-tim]

welcome to pf!

hi melihaltintas! welcome to pf!

don't try to put forum tags inside latex! …​

\int_{0}^{\infty}\int_{0}^{ \infty}\int_{0}^{\infty}e^{-\sqrt{x^2+y^2+ z^2}}\,dxdydz

 

[melihaltintas]

thanks a lot :)