You don't need to use Calculus at all. The line y= 3x, from x= 0 to 1, rotated around the x-axis, gives a cone with "height" 1 and base radius 3(1)= 3. The lline y= 2x, from x= 0 to 1, rotated around the x-axis, cone with "height" 1 and base radius 2(1)= 2. Look up the formula for volume of a cone, find each of those areas, and subtract the inner cone from the outer cone.
If you really want to use Calculus, you can use the "washer method". The a vertical line between those two lines, rotated around the x-axis will form a "washer", a disk with a hole in it. Its area is the are between the two cirles, . Its thickness, dx, gives volume . Integrate that from x= 0 to 1.