Calc 2 Final Equations

Area between curves: If: y=f(x) A=

⌠(top) - (bottom)

Area between curves: If: x=g(y) A=

⌠(right) - (left)

Volume: if function touches axis of rotation with no gap V=

Disk: π⌠(radius)²

Volume: if y = f(x)

bounds = x-values

Volume: if y = f(x) radius =

y = f(x)

Volume: if x = g(y)

bounds = y-values

Volume: if x = g(y) radius =

x = g(y)

Volume: if gap is left between axis of rotation:

Washer = π⌠(outer)² - (inner)²

Washer: if rotating x-axis

bounds = x-axis

Washer: if rotating y-axis

bounds = y-axis

Shell volume x-axis=

2π ⌠y(g(y))

Shell volume y-axis=

2π ⌠x(f(x))

Arc Length=

⌠√1 + (dy/dx)²

Surface Area =

2π⌠(variable opposite axis of rotation) *(√1 + (dy/dx)² )

I.B.P =

u⌠v - ⌠vu’

Displacement =

⌠v(t) dt

Distance =

-⌠v(t) + ⌠v(t)