natahan344
New member
- Joined
- Aug 13, 2016
- Messages
- 1
Evaluate volume integral of x^2*y over a tetrahedral volume bounded by planes x=0,y=0,z=0 and 1=z+y+z.
I am having trouble wrapping my head around the bounds to assign for this volume integral. The bounds I do use end up extremely messy when I try to carry out the integration.
I have tried using the bounds 1-x-y < z < x^2*y , 1-x/x^2+1 < y < 1-x , and 0 < x < 1 , dz dy dz by equating both functions to z then each-other for the function of intersection on the x-y plane of y= 1-x/x^2 + 1.
Also tried rearranging and changing the order to dy dz dx after rearranging the equations which led to a more complicated integral ( 0 < z < (-x^3-x^2/x^2 + 1)).
Are my choices of bounds correct and is there a way to simplify the system?
I am having trouble wrapping my head around the bounds to assign for this volume integral. The bounds I do use end up extremely messy when I try to carry out the integration.
I have tried using the bounds 1-x-y < z < x^2*y , 1-x/x^2+1 < y < 1-x , and 0 < x < 1 , dz dy dz by equating both functions to z then each-other for the function of intersection on the x-y plane of y= 1-x/x^2 + 1.
Also tried rearranging and changing the order to dy dz dx after rearranging the equations which led to a more complicated integral ( 0 < z < (-x^3-x^2/x^2 + 1)).
Are my choices of bounds correct and is there a way to simplify the system?