Not to resurrect the dead but haven't hopped on here in a bit and just wanted to say thanks all again, really. I see what I was doing wrong, but also see that it was a confusingly phrased question, which definitely gives some comfort. I very much appreciate how the discussion's helped break...
Thank you all. I see and am able to work this out properly with the above. I'm evidently a goofball, because I have no idea now how I got the right answer using only 2 - 4 (twice!). But doing from scratch a few times and keeping the above in mind, I can now see what's going on and at least...
Thanks guys. PeroK, can def confirm that the question sets the x boundaries at 0 and 4 and just states the boundary of y=0, pretty much formatted exactly as in the "Relevant Equations" above, carets aside. If it sounds like it might just be a poorly or improperly defined question, I'm happy to...
I have managed to get the answer given by the textbook I'm referencing: 3π (∛4) (1 + 3∛3)
However, this took multiple attempts, as I was initially trying to integrate within domain x = 0 - 2. This is the area for the bit that's above the x-axis (y=0 as specified). But the above answer is...