Question

Use disks and washers to find the volume of the solid the results when the area of the region y=x^3 y = 0, and x = 2 is revolved about the line x= 2

Answer 1

The functions that define the region in consideration are given below:

`\begin{gathered} y=x^3 \\ y=0 \\ x=2 \end{gathered}`

The Washer Method:

- Plotting these functions would help us visualize the question better. This is done below:

- The question would like us to revolve around the region about line x = 2. The region is bounded by the Blue, Red, and Green line. This requires that we use the formula given below:

`\begin{gathered} V=\int ^b_a{f(y)\mathrm{dy}} \\ \text{where,} \\ a\text{ and }b\text{ are the bounds of the integration along the y-axis} \end{gathered}`

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We can represent the region bounded by the function by rearranging the functions as follows: