Definite Integral 2
Figure
Figure
- Volume of a Solid
Figure
If R is a type I region bounded by x = a, x = b,
y = h(x), y = g(x), then
If R is a type II region bounded by y = c, y = d,
x = q(y),
x = p(y), then
If f(x, y) ≥ g(x, y) over a region R, then the volume
of the solid between z1 = f(x, y) and z2 = g(x, y) over
R is given by
- Area and Volume in Polar Coordinates
If S is a region in the xy-plane bounded by θ = α,
θ = β, r
= h(θ), r = g(θ), then
Figure
- Surface Area
- Mass of a Lamina
Where the lamina occupies a region R and its density
at a point (x, y) is ρ(x, y).
- Maments
The moment of the lamina about the x-axis
is
The moment of the lamina about the y-axis is
The moment of the inertia about the x-axis is
The moment of the inertia about the y-axis
is
The moment of the inertia is
- Center of Mass
- Charge of a Plate
Where electrical is distributed over a region R and
its charge
density at a point (x, y) is σ (x, y).
- Average of a Function
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