A solid is formed when the area bounded by y=8-0.5x^2, x=0 and y=0 is rotated about the y axis. Determine the volume of the solid.
How do I go about solving this?
intersects the x-axis at x = 4.
So by method of cylindrical shells, we have:
where A(x) is the surface area of the cylinder
If you make a quick sketch of the graph, you'll see it's an inverted parabola. If you imagine drawing one of the cylinders from the y-axis, you'll see that the radius is the horizontal distance from the y-axis to the curve which is just simply x. The height of the cylinder is the distance from the x-axis to the curve (which is simply the curve it self).
So:
Edit: Ok too slow xD