Area and Revolution

This calculator finds the area between curves and in polar coordinates, the volume of a solid of revolution and the surface area of revolution. The integrals are numerical.

S = ∫|f − g| dx,   S = ½∫r² dφ,   V = π∫f² dx,   S = 2π∫|f|√(1 + f′²) dx

Example. The area between y = x² and y = 2x is 4/3. Rotating y = √x on [0, 4] gives a volume of 8π.