Question

How do you find the volume of the region bounded by `y=x^2`, `y=4` and `x=0` and rotated about the y-axis?

Answer 1

Sketch the region as described in the problem and consider an element xdy extending from the y axis to the curve y=`x^2` in this region. Now using disc method form the volume integral as follows:

V= `int_0^4 pix^2dy`

= `int_0^4 piydy` , substituting `x^2`=y

=`pi/2 | y^2 |_0^4`
= 8`pi`