Expert: Sherry Wallin - 12/10/2008

Question
1. Determine the volume of the solid of revolution obtained when the curve

F(x) =x2+5

Is rotation one revolution about the x axis, between the limits x=1 and x=3


Answer

Please see additional info below:

Hi Emer~
    I am going to assume you mean by x2: x-squared.
The basic formula for volume is the integral from a to b of (pi)(f(x))squared
your function f(x) = x^2   5 squared is x^4 10x^2   25
so int(3 to 1)(pi)(x^4 10x^2   25)dx =(pi)int(3 to 1)(x^4 10x^2   25)dx
= pi(x^5/5 (10/3)x^3 25x)evaluated from 3 to 1 ie.
pi(3^5/5 (10/3)3^3 25*3)-(1^5/5 (10/3)1^3 25*1)

I am sure you can do the arithmetic from here.

Math Prof

I am sorry about the operation (+) not showing up, the website was having difficulties when a person used spell check it removed the symbols. The problem is now fixed.

Math Prof