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# Core 3 Volumes of Revolution watch

1. The question asks to find the Volume generated when the region bounded by the curves y = 2x^2 and the line y= 3 - x^2 is rotated 180 degrees about the y-axis.

I have no idea what limits to use or how to start since the region bounded crosses over the y-axis. I tried using integrating both between y=0 and y=3, and then take one away from each other but that came up with the wrong answer.

Thanks in advance for any help!

(correct answer is (3pi)/2 for reference)
2. you need to find where the curves intersect... this will help with the limits
3. the curves intersect at (1,2) and (-1,2)

but the curve region goes up to 3 along the y axis (y=3-x^2) , im not very sure at all how to go about it
4. (Original post by Mr. Ee)
The question asks to find the Volume generated when the region bounded by the curves y = 2x^2 and the line y= 3 - x^2 is rotated 180 degrees about the y-axis.

I have no idea what limits to use or how to start since the region bounded crosses over the y-axis. I tried using integrating both between y=0 and y=3, and then take one away from each other but that came up with the wrong answer.

Thanks in advance for any help!

(correct answer is (3pi)/2 for reference)
So, your shape is bounded by two curves and rotated about the y-axis.

Notice that from y=0 to 2, the boundary is 2x^2, and from y=2 to 3 the boundary is 3-x^2.

So, you'll need to set up two integrals, one for each part of the shape.
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5. (Original post by ghostwalker)
So, your shape is bounded by two curves and rotated about the y-axis.

Notice that from y=0 to 2, the boundary is 2x^2, and from y=2 to 3 the boundary is 3-x^2.

So, you'll need to set up two integrals, one for each part of the shape.
Thank you thats sorted it out

much appreciated!

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