Integration of Function of Two Variables

[PeterFer]

Homework Statement

For one of my physics classes I need to integrate a function of two variables, but I haven't learned how to do it yet in my calculus classes. If anyone could explain to me how to do it, it would be much appreciated. It's probably pretty simple I just haven't learned it yet.

the integral is $$\int$$ (z ² + x²)^-3/2 dx



and i know that the answer is x/ sqrt (z² + x²) z²


thanks

 

[Char. Limit]

Homework Statement

For one of my physics classes I need to integrate a function of two variables, but I haven't learned how to do it yet in my calculus classes. If anyone could explain to me how to do it, it would be much appreciated. It's probably pretty simple I just haven't learned it yet.

the integral is $$\int$$ (z ² + x²)^-3/2 dx

and i know that the answer is x/ sqrt (z² + x²) z²


thanks

z^2 is a constant with respect to x. That might help.

 

[PeterFer]

yea I've been trying to think of it that way but everything i do doesn't end up working and I can't think of anything else to do

 

[╔(σ_σ)╝]

You can make a trig substitution.

 

[PeterFer]

I think I understand where the sqrt(z² + x²) in the denominator of the answer comes from, if you pretend z² + x² is one term and take its anti-derivative you get 1/sqrt(z² + x²), but i don't know where the x in the numerator or the z² in the denominator come from

 

[╔(σ_σ)╝]

What happens if you make x= ztan$$\theta$$.

 

[PeterFer]

What happens if you make x= ztan$$\theta$$.

oh wow thank you so much, I completely forgot about trig substitution. Thanks a lot I just got it