Expert: Ahmed Salami - 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
Hi Emer,
The volume of the solid of revolution obtained when f(x) is rotated about the x axis between x = a and x = b is the definite integral of #[f(x)]^2 .dx from a to b.
where # represents pi
For f(x) = x^2 + 5  between the limits x=1 and x=3
{#[f(x)]^2 .dx   (from a to b)
= #{(x^2 + 5)^2 .dx   (from 1 to 3)
= #{(x^4 + 10x^2 + 25)dx   (from 1 to 3)
= #[(x^5)/5 + (10x^3)/3 + 25x] (from 1 to 3)
= #[(3^5)/5 + (10.3^3)/3 + 25.3] - #[(1^5)/5 + (10.1^3)/3 + 25.1]
= #[243/5 + 90 + 75] - #[1/5 + 10/3 + 25]
= 2776#/15 square units

Regards