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!

please help!

thanks

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?

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! :/

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?