A surface integral generalizes integration from lines to surfaces by calculating quantities like flux or mass over a given surface. It integrates a function over the surface and is denoted by the symbol ∮ or ∫∫. The general form is the integral of a function f(x, y, z) over the surface S, where S is the surface of integration and f is the integrand, or function being integrated.

2. • A surface integral is a type of integral that extends the
concept of integration from one dimension (line integrals) to
two dimensions over a surface. It
• involves integrating a function over a given surface to
calculate quantities such as flux, mass, or other physical
properties.
Surfaceintegral.

3. The surface integral
is typically denoted
by the symbol ∮ or ∬
and is defined over a
closed surface S.
The general form of a
surface integral can be
expressed as follows:
∬_S f(x, y, z) dS

4. where:
S represents the surface over
which the integral is
performed.
F(x, y, z) is the integrand, which
is a function of the spatial
variables x, y, and z.
dS represents an infinitesimal

5. The formula for the surface integral of a vector field F over a
surface S is given by:
∫∫S F · dA,
where the integral is taken over the surface S, and dA
represents the differential area vector pointing outward from
the surface.
Vector field:-

6. The formula for the
surface integral of a
scalar field f over a
surface S is given by:
∫∫S f dA,
where the integral is
taken over the surface S,
and dA represents the
differential area vector
pointing outward from
the surface
Scalar field:-