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