# Volume of Revolution question!

• Apr 18th 2013, 11:59 PM
Luke2806
Volume of Revolution question!
The normal to the curve y=3x^2+2 at the point B(1,5) meets the x-axis at the point C.
The finite region bounded by the curve, the line BC and the y-axis is rotated through 2pi radians about the x-axis
Find the volume of the solid of revolution generated?

So i really can't get my head around this!
But this is what i did..

V = ∫[0 to 1] πy^2 dx
= ∫[0 to 1] π(3x^2 + 2)^2 dx
= ∫[0 to 1] π(9x^4 + 12x^2 + 4) dx
= π[(9/5)x^5 + (12/3)x^3 + 4x)]|[0 to 1]
= π[(9/5)x^5 + 4x^3 + 4x)]|[0 to 1]
= π[(9/5)*1 + 4*1 + 4*1]
= π[(9+40)/5]
= 49π/5

i do believe that theres more to it and that's not simply the answer, but i really don't have clues!
thanks
• Apr 19th 2013, 12:24 AM
MarkFL
Re: Volume of Revolution question!
For x = 0 to x = 1, the disks do have a radius described by the given parabola, but you need to let the disks have a radius given by the normal curve from x = 1 until the x=intercept of the normal line. Can you give the equation of the normal line?
• Apr 19th 2013, 04:35 AM
Luke2806
Re: Volume of Revolution question!
Quote:

Originally Posted by MarkFL
For x = 0 to x = 1, the disks do have a radius described by the given parabola, but you need to let the disks have a radius given by the normal curve from x = 1 until the x=intercept of the normal line. Can you give the equation of the normal line?

So is the normal equation
y=-x+1 ?

I still don't quite grasp it! :/
• Apr 19th 2013, 10:43 AM
MarkFL
Re: Volume of Revolution question!
Quote:

Originally Posted by Luke2806
So is the normal equation
y=-x+1 ?

I still don't quite grasp it! :/

No, you want to find the slope of the tangent line at the given point, the use the negative reciprocal of that, and then use the point-slope formula to determine the normal line. What is the slope of the tangent line?