Volume of revolution

Question

Hi, for some of the problems Im doing, I have to rewrite the y function in terms of x. So for example, y=x^3 about the y axis. The only thing I dont get is the rewritting it into x. The solution is x^2=y^(2/3) but I dont know how to get to this answer. Also, Ive been trying to find a video on youtube but cant find any. I tried to type in " rewritting y as x " but its not what Im looking for. 

Answer 1

The volume of revolution using a disk method will use an integrand of pi*r²

 

where r is the radius of rotation

 

In this problem, mark is correct, take y = x³  and solve for x by taking the cube root of both sides.

Therefore, y^1/3 =x

 

y^1/3 would be the distance (radius) from the curve to the y-axis.

 

we square it because of the original formula pi*radius-squared

 

y₂

∫pi(y^2/3) dy    all you need now is the upper and lower value of y.

y₁

Answer 2

y = x³ is a function. To write x in terms of y, you would determine the inverse, y^1/3 = x. Yet this is not a function. To make it a function either the domain must be restricted or both sides are squared, (y^1/3)² = x².