Triple Integral z = 4-x^2, y+z=5...

[Whitesttax]

Hello.
Here's my problem:

triple integrate of (x-1), 
the region of integration is delimited by planes y = 0, z = 0, y + z = 5 
and the equation z = 4 -x^2

I've spent 2 hours+ trying different combinations but nothing seems to work.

I tried to divide it in 2 integrals (which I think it's right since z has 2 different equations > from y=0 to y=1 and then y=1 to y=5)

I tried dzdxdy, dzdydx...

One thing I might be doing wrong is to find the plane xy, I do the interception of z = 5 - y and z = 4 - x^2 which gives me y = 1 + x^2
Is this right? Could you help me formulate the integration limits, please?

The answer is -544/15

 

[Deleted member 4993]

Hello.
Here's my problem:

 [B]triple integrate of (x-1), the region of integration is delimited by planes y = 0, z = 0, y + z = 5 and the equation z = 4 -x^2[/B]

I've spent 2 hours+ trying different combinations but nothing seems to work.
I tried to divide it in 2 integrals (which I think it's right since z has 2 different equations > from y=0 to y=1 and then y=1 to y=5)
I tried dzdxdy, dzdydx...
One thing I might be doing wrong is to find the plane xy, I do the interception of z = 5 - y and z = 4 - x^2 which gives me y = 1 + x^2
Is this right? Could you help me formulate the integration limits, please?
The answer is -544/15

What are the limits of integration - that you had found?