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C3 Volume of Revolution

volume.jpg
I've been able to do all the other questions with easy, simply using the two formulas - when it's rotated about the x-axis, the limits of the integral are given as the lines x=a and x=b. Similarly, when it's rotated about the y-axis the limits are y=c and y=d...

However in part b) for both question 8 and 9, the curves are being rotated about the x-axis yet the line y=k is also specified. How am I meant to go about this?

Thanks.

TLDR question 8)b) and 9)b) are different from all the rest. Help please!
Original post by edd1234
volume.jpg
I've been able to do all the other questions with easy, simply using the two formulas - when it's rotated about the x-axis, the limits of the integral are given as the lines x=a and x=b. Similarly, when it's rotated about the y-axis the limits are y=c and y=d...

However in part b) for both question 8 and 9, the curves are being rotated about the x-axis yet the line y=k is also specified. How am I meant to go about this?

Thanks.

TLDR question 8)b) and 9)b) are different from all the rest. Help please!


Let's do 9b:

Integrate y^2=x+4 between x=0 and x=5.

Now integrate the square of y=(3/5)x between the same values - so you would be integrating (9/25)x^2 between x=0 and x=5.

Now take this volume and subtract it from the volume of PQ...

So Volume(PQ) - Volume(y=3x/5) = Volume of region R.
(edited 8 years ago)
Original post by ALevelBro
Let's do 9b:

Integrate y^2=x+4 between x=0 and x=5.

Now integrate the square of y=(3/5)x between the same values - so you would be integrating (9/25)x^2 between x=0 and x=5.

Now take this volume and subtract it from the volume of PQ...

So Volume(PQ) - Volume(y=3x/5) = Volume of region R.


ahh, that makes a lot of sense. thanks.

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