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# a level maths core 3 question solids of revolution watch

1. Question: The region n R bounded by the curve y=x((x^3)+1)^3, the x-axis between 0 and 1, and the line x=1, is rotated through 2pi radians about the x-axis. Find the volume of the solid of revolution formed.
How would you go about the question, you`ll have to get the equation into y^2 first, but how would you do that? expand all the brackets or am i missing something?
2. (Original post by itlstallion69)
Question: The region n R bounded by the curve y=x((x^3)+1)^3, the x-axis between 0 and 1, and the line x=1, is rotated through 2pi radians about the x-axis. Find the volume of the solid of revolution formed.
How would you go about the question, you`ll have to get the equation into y^2 first, but how would you do that? expand all the brackets or am i missing something?
try the substitution of u=x^3+1
3. (Original post by itlstallion69)
Question: The region n R bounded by the curve y=x((x^3)+1)^3, the x-axis between 0 and 1, and the line x=1, is rotated through 2pi radians about the x-axis. Find the volume of the solid of revolution formed.
How would you go about the question, you`ll have to get the equation into y^2 first, but how would you do that? expand all the brackets or am i missing something?
No need to expand.

and hence the substitution does the job when integrating it.
4. Someone link me to the fancy handwriting symbols page thingy
5. (Original post by Bulletzone)
Someone link me to the fancy handwriting symbols page thingy
lol what is that?
6. (Original post by Bulletzone)
Someone link me to the fancy handwriting symbols page thingy
Fancy handwriting symbols page thingy
7. am coming to an answer of 128pi all over 21 but the book says 127pi all over 21
8. (Original post by itlstallion69)
am coming to an answer of 128pi all over 21 but the book says 127pi all over 21
you may have forgotten to minus the 1pi/27 from the second part of the indefinite integral
9. (Original post by yusyus)
you may have forgotten to minus the 1pi/27 from the second part of the indefinite integral
yeh just noticed i disregarded the last part of the integral since the x value was zero, thanks

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