Question

How do you do this question?

Answer 1

Solution : 126π/5

Explanation:

Step 1 (Assign the 'values') : Using the cylinder method, given that x = 0 and x = 3, we will integrate along the x-axis from 0 to 3. The radius of each cylinder will be r = x, and the height should be the following,

h = y₁ - y₂ = x³ - 8

Step 2 (Substitute) : Remember that the volume of the graph will be in the following form,

`\mathrm{V\:=\:2\pi \int _a^b\:rhdx}`

If we substitute known values we should go in the following both. Remember that r = x, h = x³ - 8, b = 3, and a = 0 (our limits). Take a look at the attachment for those calculations. As you can see our solution is 126π/5.