Volume of Revolution Y1

Formula for Area Under a Positive Curve

∫^b_a y dx

where y = f(x) is the equation of the curve

Formula for a Rotation of 2π About the x-axis

π∫^b_a y² dx

Formula for a Rotation of 2π About the y-axis

π∫^b_a x² dy

Volume of a Cylinder

height h and radius r

V = πr²h

Volume of a Cone

height h and base radius r

V = (1/3)πr²h

Adding or Subtracting Volumes

you can find more complicated volumes of revolution by adding or subtracting volumes