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 :)