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# Core Maths 3: Integration to find volume of revolution ii

1. Hi there

Please could you help me with this one:

I have tried integrating both the line and the curve for the value of x = 8, and I am getting 2 pi for the area under the curve and 32 pi for the area under the line y = 2, the answer I have in my book for the whole thing is 18 pi.

I don't really know how to work out the shaded area, any ideas??
2. 32pi is wrong for your cylinder ... I think you have used 8 instead of 6
3. The curve is wrong too

Not sure how you have got the 2pi
4. When you integrated you say you used 8

5. (Original post by jackie11)
Hi there

Please could you help me with this one:

I have tried integrating both the line and the curve for the value of x = 8, and I am getting 2 pi for the area under the curve and 32 pi for the area under the line y = 2, the answer I have in my book for the whole thing is 18 pi.

I don't really know how to work out the shaded area, any ideas??
Required volume
6. (Original post by jackie11)
Hi there

Please could you help me with this one:

I have tried integrating both the line and the curve for the value of x = 8, and I am getting 2 pi for the area under the curve and 32 pi for the area under the line y = 2, the answer I have in my book for the whole thing is 18 pi.

I don't really know how to work out the shaded area, any ideas??
Use the reverse bracket rule when integrating and you should end up with 18 -0 when you sub in the 8 and 2 hence 18pi.

I just tried it out on a piece of paper and got the right answer.
7. (Original post by raheem94)
Required volume
I find it odd that both the OP and yourself would use integration to find the volume of a cylinder
8. (Original post by TenOfThem)
32pi is wrong for your cylinder ... I think you have used 8 instead of 6

(Original post by TenOfThem)
The curve is wrong too

Not sure how you have got the 2pi

(Original post by TenOfThem)
When you integrated you say you used 8

I did use 8, I didn't use another limit as I assumed it was 0
9. (Original post by raheem94)
Required volume
aww thank you, this is great!!!
10. (Original post by jackie11)
I did use 8, I didn't use another limit as I assumed it was 0
Firstly ... just looking at the diagram you should have realised that the other limit was 2

Secondly ... even when a limit is 0 you cannot just ignore it as the value may not always be 0
11. (Original post by TenOfThem)
I find it odd that both the OP and yourself would use integration to find the volume of a cylinder
Integration here takes the same time as using the area of cylinder takes, so i prefer to use integration rather than
12. (Original post by raheem94)
Integration here takes the same time as using the area of cylinder takes [/latex]
really?

pi x 4 x 6 does not really take any time
13. (Original post by TenOfThem)
really?

pi x 4 x 6 does not really take any time

The above will also not take much time, may be just 5 seconds more.
14. (Original post by raheem94)

The above will also not take much time, may be just 5 seconds more.
Much more scope for error though ... not saying that you are wrong ... just that I find it odd
15. (Original post by TenOfThem)
Much more scope for error though ... not saying that you are wrong ... just that I find it odd
Still the probability of error in such a question will be very less. This is basic integration.
16. (Original post by raheem94)
Still the probability of error in such a question will be very less. This is basic integration.
Given the errors made by the OP I beg to differ
17. (Original post by TenOfThem)
Given the errors made by the OP I beg to differ
Actually i was indicating my case not the OP's. I have seen several simple integration mistakes made by the OP so its best for the OP to avoid integration as much as possible.

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