a level maths core 3 question solids of revolution

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?

Reply 1

yusyus

21

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

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?