Evaluate the triple integral for specified function

[musicmar]

Homework Statement

Evaluate the triple integral for specified function and box B.

f(x,y,z) = x e^y-2z
0<x<2, 0<y, z>1
(The < and >'s should be less than or equal to but, I don't know how to write that here)

Homework Equations

The Attempt at a Solution

I know how to evaluate iterated integrals, but I am confused by the bounds in this problem. y and z only have one bound, so I don't know how to set up the integral.

 

[jackmell]

y and z only have one bound, so I don't know how to set up the integral.

Why don't they just go to infinity then? Why not just take a stab at it and say, let's integrate dzdydx and try anyway to set up reasonable limits? If z>1 then it's limits should be (1,infty}, same dif with y, (0,infty), and x goes from 0 to 2. Here goes:

$$\int_0^2 \int_0^{\infty}\int_1^{\infty} xe^{y-2z} dzdydx$$

Now, I haven't tried to integrate that. Maybe when we do, we'll get into a tough integrand to handle. Then may want to consider a different integration order if that would make the integration easier.

 

[Mark44]

Homework Statement

Evaluate the triple integral for specified function and box B.

f(x,y,z) = x e^y-2z
0<x<2, 0<y, z>1
(The < and >'s should be less than or equal to but, I don't know how to write that here)

Use <= for less than or equal to, and >= for greater than or equal to.

Homework Equations

The Attempt at a Solution

I know how to evaluate iterated integrals, but I am confused by the bounds in this problem. y and z only have one bound, so I don't know how to set up the integral.

There are implied bound for y and z.

0 <= y < infinity
1 <= z < infinity

Do you know what the region in this problem looks like?

 

[musicmar]

Thank you. Is it a rectangular prism? y >= 0 is a plane bounded by x, and z would provide the height. But does this help me integrate it?

 

[Mark44]

See jackmell's post.

 

[MADW]

I had to work the same problem. I have found discrepancies in the book before regarding notation, so when I couldn't solve the problem I assumed the boundary meant 0≤X≤2; 0≤y,z≤1→0≤y≤1; 0≤z≤1. Alternately, the box B=[0,2], [0,1], [0,1]. When I worked the problem with these boundaries I got the same answer as the book.
Hope it helps.
Also, you can get "less than or equal to" by underlining the "less than" symbol.

 

[Ray Vickson]

Homework Statement

Evaluate the triple integral for specified function and box B.

f(x,y,z) = x e^y-2z
0<x<2, 0<y, z>1
(The < and >'s should be less than or equal to but, I don't know how to write that here)

Homework Equations

The Attempt at a Solution

I know how to evaluate iterated integrals, but I am confused by the bounds in this problem. y and z only have one bound, so I don't know how to set up the integral.

You can write <= and >=, or else you can click on the "Quick symbols" from the panel at the side of the input window, to get ≤ and ≥.

RGV