We are given:
Sketch the solid whose volume is given by the iterated
integral.
$$\int_{0}^{1}\int_{0}^{1}(4-x-2y)dxdy$$
I arrived at $-11/2$. However, we are asked to sketch the solid. I do not know how to do this freehand (or with TI-89 for what its worth). If someone could provide a reference to how it would help tremendously.
Best Answer
If you have heard contour map, which may appear in your geography class. Think the solid as a mountain and draw the $\color{red}{contour\ line}$ first. Steps to draw contour line(in a two dimension axes): $$z=f(x,y)=4-x-2y$$ let $z=0$ then draw $$0=4-x-2y$$ let$z=0.5$ then draw $$0.5=4-x-2y$$ let$z=1$ then draw $$1=4-x-2y$$ Once you get a contour line graph then you can imagine to draw a solid, which seems not so hard to draw in this case.
Finally, if you want to check your graph, go to http://www.wolframalpha.com/input/?i=z%3D4-x-2y