As you may know, the general formula to find the surface area generated by revolving a curve about the x-axis is the following:
***Note that everything should be in terms of x as we are integrating with respect to x.
As the limits of integral equals to 1 and 3, f'(x) equals to (0.5x^(-0.5) - 0.5x^(0.5)) and radius r equals to y, which equals to sqrt(x) - 1/3 * x^(3/2), we can change the integral with respect to x like this:
When this integral is computed (you can use a calculator), the exact answer equals to 16pi/9.
Hi,
Thank you for your question.
As you may know, the general formula to find the surface area generated by revolving a curve about the x-axis is the following:
***Note that everything should be in terms of x as we are integrating with respect to x.
As the limits of integral equals to 1 and 3, f'(x) equals to (0.5x^(-0.5) - 0.5x^(0.5)) and radius r equals to y, which equals to sqrt(x) - 1/3 * x^(3/2), we can change the integral with respect to x like this:
When this integral is computed (you can use a calculator), the exact answer equals to 16pi/9.
Does this answer your question?