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a level maths core 3 question solids of revolution watch

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    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?
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    (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
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    (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.

    y^2=x^2(x^3+1)^6 and hence the substitution u=x^3+1 does the job when integrating it.
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    Someone link me to the fancy handwriting symbols page thingy
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    (Original post by Bulletzone)
    Someone link me to the fancy handwriting symbols page thingy
    lol what is that?
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    (Original post by Bulletzone)
    Someone link me to the fancy handwriting symbols page thingy
    Fancy handwriting symbols page thingy
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    am coming to an answer of 128pi all over 21 but the book says 127pi all over 21
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    (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
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    (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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