- #1

HermGnos

- 4

- 3

- Homework Statement
- Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the y-axis:

- Relevant Equations
- x^2 + y^3 = 4, x=0, x=4, y=0

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 only gotten when domain x = 2 - 4 is used. This span would seem equally valid, just making y=0 the upper limit of y.

My real question is just: is there something in the question / format of the equations above that should have clued me in to the fact that we're integrating the data under y=0 rather than above it? It seems like every other question in this book with a similar format that only mentioned a single x=0 or y=0 and no other corresponding value for x or y was using the =0 as the lower limit, so I'm wondering if I'm missing something here that should have clued me in.

Apologies also for what's probably very imprecise math language in the question above.

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 only gotten when domain x = 2 - 4 is used. This span would seem equally valid, just making y=0 the upper limit of y.

My real question is just: is there something in the question / format of the equations above that should have clued me in to the fact that we're integrating the data under y=0 rather than above it? It seems like every other question in this book with a similar format that only mentioned a single x=0 or y=0 and no other corresponding value for x or y was using the =0 as the lower limit, so I'm wondering if I'm missing something here that should have clued me in.

Apologies also for what's probably very imprecise math language in the question above.