Find the volume of the solid generated???

Question

Let R be the region bounded by two curves described below. Find the volume of the solid generated when R is revolved about the x-axis.

 

 

 

y=2x

y=16 4√x

Answer 1

For Disc method:

 

 

 

For Shell Method

 

 

 

Answer 2

Hi Daniel,

 

In order to understand some of what is said below first visit:

 

https://www.desmos.com/calculator/6qtfjhdasg

 

Likely you want to use the "washer" method to find the volume of the solid generated. 

 

The "orange" line segment in the graph is an example "outer radius". The "black" line segment is an example of the "inner radius".

 

Setting up the integral using the washer method results in:

 

π∫¹⁶₀ [(16x^1/4)² - (2x)²]dx

 

The above shows "outer radius squared" minus "inner radius squared". 

 

Hopefully you can take it from there.

 

Answer: 16384π/3