Hello, I'm back again. I have three problems (two with two parts) that, if you guys wouldn't mind, I would like to have checked. If anything is wrong, I would highly appreciate it if you showed me where I went wrong and how to do it correctly. Thanks infinitely in advance.

Let R be the region bounded by the semicircle y = and the x-axis.

Problem 1.

a.Derive the formula for the volume of a sphere of radius r by revolving R about the x-axis using the disk method or the shell method.

My Solution (Using Disk Method)

V = dx = =

b.Derive the formula for the surface area of a sphere of radius r by revolving R about the x-axis.

My Solution (I don't know how to integrate this, please help!)

A = dx = ???

Problem 2.Let R be the region bounded by the lines x = 0, x = h, y = 0, and y = x, where r and h are positive constants.

a.Derive the formula for the volume of a right circular cone of radius r and altitude h by revolving R about the x-axis using the disk method or the shell method.

My Solution (Using Disk Method)

dx = dx = =

b.Now derive the formula for the surface area of such a cone, again, by revolving R about the x-axis.

My Solution

A = dx = dx = = =

Problem 3.Calculate the length along the curve y = 1 + from (0,1) to (4,9).

My Solution

L = dx = dx = dx = = = 8 - =

Once again, thank you.