Solve triple integral and draw its graph

[a157]

I tried solving it. But my graph is incorrect and integration limits are wrong
The integral to solve


My attempt

 

[Dr.Peterson]

I tried solving it. But my graph is incorrect and integration limits are wrong
The integral to solve
View attachment 23807

My attempt
View attachment 23808

The first three constraints represent vertical planes. The other two represent horizontal planes. You've drawn none of them! (Well, maybe z=0.)

Give the drawing another try, before trying the limits of integration again. You might try first drawing a top view, looking down at the xy-plane, before trying it in 3D.

But I hope you also see that your limits of integration have nothing to do with what you drew anyway.

 

[a157]

The first three constraints represent vertical planes. The other two represent horizontal planes. You've drawn none of them! (Well, maybe z=0.)

Give the drawing another try, before trying the limits of integration again. You might try first drawing a top view, looking down at the xy-plane, before trying it in 3D.

But I hope you also see that your limits of integration have nothing to do with what you drew anyway.

I have another try:


My current answer is exp(2)-3

 

[Dr.Peterson]

I have another try:
View attachment 23822

My current answer is exp(2)-3

The graph and limits now look good. I don't get quite the same answer (which could be my error); can you show your work for the integral?