Use a double integral to find volume of solids ?

[CalleighMay]

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help!

 

I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P

 

Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help?

 

We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book.

 

The problem is on pg 998 in chapter 14.2 in the text, number 26. It reads:

 

Use a double integral to find the volume of the indicated solid:

And it gives a picture of a solid with the vertices's: (0,0,0), 2,0,0), (0,2,0) and (0,0,2).

The solid is given the equation: x+y+z=2

 

I looked at similar problems in the same section and came up with a few ideas as to how to get started. This is what i came up with.

Making a sketch of the side on the xy-plane, i have the line: y=-x+2

Then the integral from 0 to 2 of the integral of 0 to (-x+2) of (this is where i get confused)

 

I get confused from here...

 

Any help would be greatly appreciated. Thanks guys