Volumes of Solids of Revolution

[MAC5494]

Question


I'm really having issues grasping the Volumes of Solids of revolution. I could use some help solving this question, it isn't very hard.

1. Let R be the region bounded by y = x² and y = x + 2. Find:

a) the area of R

b) the volume of the solid if R is rotated about the x-axis

c) the volume of the solid if R is rotated about the the line x = 4

Homework Equations

The Attempt at a Solution

Basically this is what I've gotten.



a)
Area = ∫((x+2)-(x²))dx
= (x²/2 + 2x) - (x³/3), evaluated over the interval (-1,2)
= 4.5


b) this is what I did but I don't know if it is right

∏∫((x+2)² - (x²))dx
= ∏∫((x²+4x+4) - x⁴) dx
= ∏(x⁵/5 - x³/3 -2x² -4x) evaluated from (-1,2)
= 72∏/5

c) I'm not sure how to start this one.

 

[jackarms]

a and b look right. For c, have you learned the shell method for integration?