Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Courses/Grayson_College/Prealgebra/Book%3A_Prealgebra_(OpenStax)/09%3A_Math_Models_and_Geometry/9.09%3A_Solve_Geometry_Applications%3A_Volume_and_Surface_Area_(Part_1)The surface area is a square measure of the total area of all the sides of a rectangular solid. The amount of space inside the rectangular solid is the volume, a cubic measure. The volume, V, of any r...The surface area is a square measure of the total area of all the sides of a rectangular solid. The amount of space inside the rectangular solid is the volume, a cubic measure. The volume, V, of any rectangular solid is the product of the length, width, and height. To find the surface area of a rectangular solid, find the area of each face that you see and then multiply each area by two to account for the face on the opposite side.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_206.5/04%3A_Polynomial_and_Rational_Functions/4.09%3A_Inverses_and_Radical_FunctionsIn this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process.
- https://math.libretexts.org/Courses/Las_Positas_College/Foundational_Mathematics/08%3A_Geometry_and_Graphing/8.03%3A_Solve_Geometry_Applications-_Volume_and_Surface_Area_(Part_1)The surface area is a square measure of the total area of all the sides of a rectangular solid. The amount of space inside the rectangular solid is the volume, a cubic measure. The volume, V, of any r...The surface area is a square measure of the total area of all the sides of a rectangular solid. The amount of space inside the rectangular solid is the volume, a cubic measure. The volume, V, of any rectangular solid is the product of the length, width, and height. To find the surface area of a rectangular solid, find the area of each face that you see and then multiply each area by two to account for the face on the opposite side.
- https://math.libretexts.org/Courses/University_of_California_Davis/UCD_Mat_21D%3A_Vector_Analysis/Integration_in_Vector_Fields/16.5%3A_Surfaces_and_Area\[\begin{align}|v \times w| &= |ˆiˆjˆkΔx0fx(x,y)0Δyfy(x,y)Δy| \\[4pt] &= | -(f_...\[\begin{align}|v \times w| &= |ˆiˆjˆkΔx0fx(x,y)0Δyfy(x,y)Δy| \\[4pt] &= | -(f_y (x,y)\Delta y\Delta x) \hat{\textbf{i}} - (f_x (x,y) \Delta y \Delta x) \hat{\textbf{j}} + (\Delta y \Delta x) \hat{\textbf{k}} | \\[4pt] &= \sqrt{f_y^2 (x,y) (\Delta y \Delta x)^2 + f_x^2 (x,y) (\Delta y \Delta x)^2 +(\Delta y \Delta x)^2 } \\[4pt] &= \sqrt{f_y^2 (x,y) + f_x^2 (x,y) +1 } \; \Del…
- https://math.libretexts.org/Courses/University_of_Maryland/MATH_241/05%3A_Vector_Calculus/5.07%3A_Surface_IntegralsIf 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.
- https://math.libretexts.org/Courses/College_of_the_Canyons/Math_130%3A_Math_for_Elementary_School_Teachers_(Lagusker)/06%3A_Geometry/6.03%3A_Area_Surface_Area_and_VolumeThink inside the box and approximate the Shaded Area: (area of a square is base times height) Think around the box (surface area) and approximate the Shaded Area: (How many sides are not seen in the p...Think inside the box and approximate the Shaded Area: (area of a square is base times height) Think around the box (surface area) and approximate the Shaded Area: (How many sides are not seen in the picture, which must be included in the final answer?) Think inside the box (volume) and approximate the Shaded Area: Volume is base time’s height times width. Explain the difference between area, surface area, and volume. Find the Surface Area of the following shapes:
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_(Kravets)/05%3A_Vector_Calculus/5.07%3A_Surface_IntegralsIf 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.
- https://math.libretexts.org/Under_Construction/Purgatory/MAT-004A_-_Multivariable_Calculus_(Reed)/05%3A_Vector_Calculus/5.07%3A_Surface_IntegralsIf 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.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.06%3A_Numerical_Integration/3.6E%3A_Exercises_for_Section_3.6This page provides exercises on approximating integrals using numerical methods like the midpoint rule, trapezoidal rule, and Simpson's rule, detailing specific integrals, subdivisions, and formats fo...This page provides exercises on approximating integrals using numerical methods like the midpoint rule, trapezoidal rule, and Simpson's rule, detailing specific integrals, subdivisions, and formats for answers. It discusses the importance of numerical methods alongside the Fundamental Theorem of Calculus and includes tasks on estimating errors, arc lengths, and areas under curves. The text also features example calculations and a sample problem using coordinates to estimate land area.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/06%3A_Applications_of_Integration/6.05%3A_Arc_Length_of_a_Curve_and_Surface_AreaThe arc length of a curve can be calculated using a definite integral. The arc length is first approximated using line segments, which generates a Riemann sum. Taking a limit then gives us the definit...The arc length of a curve can be calculated using a definite integral. The arc length is first approximated using line segments, which generates a Riemann sum. Taking a limit then gives us the definite integral formula. The same process can be applied to functions of y. The concepts used to calculate the arc length can be generalized to find the surface area of a surface of revolution. The integrals generated by both the arc length and surface area formulas are often difficult to evaluate.
- https://math.libretexts.org/Courses/Mission_College/MAT_3B_Calculus_II_(Kravets)/07%3A_Applications_of_Integration/7.04%3A_Arc_Length_of_a_Curve_and_Surface_AreaThe arc length of a curve can be calculated using a definite integral. The arc length is first approximated using line segments, which generates a Riemann sum. Taking a limit then gives us the definit...The arc length of a curve can be calculated using a definite integral. The arc length is first approximated using line segments, which generates a Riemann sum. Taking a limit then gives us the definite integral formula. The same process can be applied to functions of y. The concepts used to calculate the arc length can be generalized to find the surface area of a surface of revolution. The integrals generated by both the arc length and surface area formulas are often difficult to evaluate.
