How to sketch and find the volume of a solid from an integral

[Spectre32]

Ok I'm working on this Integral: http://home.comcast.net/~bruins83/IMG_1527.jpg

I figured the Integral to be equal to 11/2. Now they want me to graph it, and I'm slidght confused on how to go about this, The direction read, Sketch the solid whose volume is given by (integral) Find the volume.

Any help would be appericated.

Thanks

 

[stunner5000pt]

i can't see what you've posted there properly can you just type it out

 

[dav2008]

$$\int_{0}^{1} \int_{0}^{1}2-x-y~dydx$$

 

[stunner5000pt]

$$\int_{0}^{1} \int_{0}^{1}2-x-y~dydx$$

the solution to that is just one

the new function after evaluating the indefinite integral is $$\frac{-1}{2} xy (x+y-4)$$

 

[Spectre32]

Yeha I went back over it, and got one, sorry about that. Anyways, I still need help graphing it. Actually what DO i even look at to graph?

 

[stunner5000pt]

Yeha I went back over it, and got one, sorry about that. Anyways, I still need help graphing it. Actually what DO i even look at to graph?

if you want to graph (sketch) it then you have to hold Y constant and look at all the ways x can move around the axes. After that simply enclose the surface

it loos like a gentle slope down a hill and then a little rise on the positive side

 

[dav2008]

What exactly do they want you to graph? Can you quote the book exactly?

If they just want you to draw in the region over which the function is being integrated then you just take the limits and graph them on the x/y plane.

Your limits are y=0, y=1, x=0, x=1 so it would just be a square.

Edit: Never mind, I reread your post and it says to sketch the solid.