Question

How to graph this bounded region in 3d.

Answer 1

G is the solid in the first octant that is bounded by the parabolic cylinder z=2-x^2 and the plane z=0, y=x, and y=0.

Answer 2

This question consist of an integral to solve, but that's not the problem. I want to set up the limits, but to do that i have to draw so i can get an idea what intervals are present.

Answer 3

"First octant" implies that x, y and z are all zero or greater.

Answer 4

Correct.

Answer 5

"bounded by the parabolic cylinder z=2-x^2" Note that y is not mentioned here, meaning that y can have any value, but z (the vertical component of any point on the region) is a function of x with z-intercept (0,0,2). Looking at your imaginary solid along the y-axis, you should see an upside down parabola. Again, y can have any value.