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?
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
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?