Question

surface area of sqrt(5x) by rotating it from the x-axis from 0 to 3

Answer 1

Since the graph is rotated about the x-axis, you can use the formula \[V = \pi \int\limits_{x=a}^{x=b}(f(x))^2dx\]

Answer 2

What we do is that we sum of the volumes of infinitesimal cylinders with radius f(x) and width dx, so that each cylinder has volume \[\pi (f(x))^2 dx\] (remember that a circle has area \[A = \pi r^2\] and the volume of a cylinder with height h is \[V = Ah = \pi r^2h\]

Answer 3

*sum all the volumes

Answer 4

Question is asking for surface area, not volume.

Answer 5

Ooops, you are so right :D