As you may know, the general formula for calculating volumes by cylindrical shells is the following:
As the regin enclosed is revolved about the y-axis, we know that the integral should be written in terms of x. As the region is revolved about the y-axis, the radius (r) would simply be x and the height (h) would be y, which equals to x^3.
If you graph the enclosed region, it looks like this.
Hence, the limits of integrand would be 0 and 2.
With these information, we can solve for the volume using the formula provided above, which would look like this:
When you compute this integrand, the exact answer would be 12.8π.
Hi,
Thank you for your question.
As you may know, the general formula for calculating volumes by cylindrical shells is the following:
As the regin enclosed is revolved about the y-axis, we know that the integral should be written in terms of x. As the region is revolved about the y-axis, the radius (r) would simply be x and the height (h) would be y, which equals to x^3.
If you graph the enclosed region, it looks like this.
Hence, the limits of integrand would be 0 and 2.
With these information, we can solve for the volume using the formula provided above, which would look like this:
When you compute this integrand, the exact answer would be 12.8π.
Does this answer your question?