Solution
The functions that define the region in consideration are given below:
[tex]\begin{gathered} y=x^3 \\ y=0 \\ x=2 \end{gathered}[/tex]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:
[tex]\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}[/tex]-
We can represent the region bounded by the function by rearranging the functions as follows:
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