Volume of revolution formula (H2 maths)

Mad Hat SG

If the area below a curve y=f(x) from x=a to x=b is rotated 360 degrees about the x-axis, then the volume of revolution is given by:

π ∫ y² dx , with limits a and b.

But if the same area is rotated 360 degrees around the y-axis instead, then C.S. Toh (A-level study guide) gives this formula for the volume of revolution:

2π ∫ xy dx , with limits a and b.

Is this second formula in the H2 maths syllabus also? Are A-level students expected to know it? (Obviously, the first formula must be known. But this second one, I'm not so sure.)

Seowlah SG

The second formula is NOT required in the H2 syllabus as the students can use the formula π ∫ x² dy and the big volume minus the small volume to get the shaded volume.

However, the formula can come in handy as a short cut method.

Mad Hat SG

Thanks!