Volume of revolution (PU2 H2)

An area under the graph y=x^2, x=0, x=2 and the x-axis can be estimated by the area of 5 rectangle (the first one with height 0). If this 5 rectangles are rotated 360 degrees about the x-axis, 5 disc will be formed and the area are calculated as follows

Click image

If the number of rectangles between x=0 and x=2 is increased with the width of each rectangles becoming infinitely small, the exact volume generated from the revolution of the area bounded can be calculated and the value is the integral as shown above.

Please see the animation

Please see animation

We can also work out the volume of solid generated from the area between 2 graph. Below is an animation when the area bounded by y=(0.5x)^2 , y=ln(x+1) and x=2 is rotated about the x axis.