Search

3.3: Surface Integrals
https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/03%3A_Surface_Integrals/3.03%3A_Surface_Integrals
We are now going to define two types of integrals over surfaces.
5.7: Surface Integrals
https://math.libretexts.org/Courses/University_of_Maryland/MATH_241/05%3A_Vector_Calculus/5.07%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
5.7: Surface Integrals
https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_(Kravets)/05%3A_Vector_Calculus/5.07%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
5.7: Surface Integrals
https://math.libretexts.org/Under_Construction/Purgatory/MAT-004A_-_Multivariable_Calculus_(Reed)/05%3A_Vector_Calculus/5.07%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
16.6: Surface Integrals
https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_v2_(Reed)/16%3A_Vector_Calculus/16.06%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
4.4: Surface Integrals and the Divergence Theorem
https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/04%3A_Line_and_Surface_Integrals/4.04%3A_Surface_Integrals_and_the_Divergence_Theorem
We will now learn how to perform integration over a surface in $\mathbb{R}^3$ , such as a sphere or a paraboloid. Recall from Section 1.8 how we identified points $(x, y, z)$ on a curve $C$ in \...We will now learn how to perform integration over a surface in $\mathbb{R}^3$ , such as a sphere or a paraboloid. Recall from Section 1.8 how we identified points $(x, y, z)$ on a curve $C$ in $\mathbb{R}^3$ , parametrized by $x = x(t), y = y(t), z = z(t), a ≤ t ≤ b$ , with the terminal points of the position vector.
16.6: Surface Integrals
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/16%3A_Vector_Calculus/16.06%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
3.6: Surface Area
https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/03%3A_Vector_Calculus/3.06%3A_Surface_Area
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
16.7: Surface Integrals
https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/16%3A_Vector_Calculus/16.07%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.
16.7: Surface Integrals
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/16%3A_Vector_Calculus/16.07%3A_Surface_Integrals
Suppose that vector $\bf N$ is a unit normal to the surface at a point; ${\bf F}\cdot{\bf N}$ is the scalar projection of $\bf F$ onto the direction of $\bf N$ , so it measures how fast the flu...Suppose that vector $\bf N$ is a unit normal to the surface at a point; ${\bf F}\cdot{\bf N}$ is the scalar projection of $\bf F$ onto the direction of $\bf N$ , so it measures how fast the fluid is moving across the surface. $\begin{align} \iint\limits_{D} {\bf F}\cdot{\bf N}\,dS &=\iint\limits_{D}{\bf F}\cdot {{\bf r}_u\times{\bf r}_v\over|{\bf r}_u\times{\bf r}_v|} |{\bf r}_u\times{\bf r}_v|\,dA \\[4pt] &=\iint\limits_{D}{\bf F}\cdot ({\bf r}_u\times{\bf r}_v)\,dA. \end{align}$
3.7: Surface Integrals
https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q4/03%3A_Vector_Calculus/3.07%3A_Surface_Integrals
If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integ...If we wish to integrate over a surface (a two-dimensional object) rather than a path (a one-dimensional object) in space, then we need a new kind of integral. We can extend the concept of a line integral to a surface integral to allow us to perform this integration. Surface integrals are important for the same reasons that line integrals are important. They have many applications to physics and engineering, and they allow us to expand the Fundamental Theorem of Calculus to higher dimensions.

Search

Text Color

Text Size

Margin Size

Font Type

Support Center

How can we help?