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- https://math.libretexts.org/Under_Construction/Purgatory/Book%3A_Active_Calculus_(Boelkins_et_al.)/06%3A_Using_Definite_Integrals/6.04%3A_Physics_Applications_-_Work_Force_and_PressureWhile there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar ...While there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar to several others that we’ve encountered in applications of the definite integral. In particular, the basic idea is to take a difficult problem and somehow slice it into more manageable pieces that we understand, and then use a definite integral to add up these simpler pieces.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/13%3A_Non-Right_Triangle_Trigonometry/13.05%3A_Vectors_-_An_Algebraic_ApproachThis section covers vectors from an algebraic perspective, including expressing vectors in coordinate form, converting between geometric and coordinate forms, and performing vector operations such as ...This section covers vectors from an algebraic perspective, including expressing vectors in coordinate form, converting between geometric and coordinate forms, and performing vector operations such as scalar multiplication and addition. It introduces unit vectors, discusses their significance, and explores their use in practical applications like force and equilibrium problems. The section includes examples and exercises to reinforce understanding of algebraic vector manipulation.
- https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al.)/06%3A_Using_Definite_Integrals/6.04%3A_Physics_Applications_-_Work_Force_and_PressureWhile there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar ...While there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar to several others that we’ve encountered in applications of the definite integral. In particular, the basic idea is to take a difficult problem and somehow slice it into more manageable pieces that we understand, and then use a definite integral to add up these simpler pieces.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus_Lecture_Notes_(Simpson)/01%3A_Applications_of_Integration/1.05%3A_WorkIn this section, we examine some physical applications of integration. Several physical applications of the definite integral are common in engineering and physics. Definite integrals can be used to d...In this section, we examine some physical applications of integration. Several physical applications of the definite integral are common in engineering and physics. Definite integrals can be used to determine the mass of an object if its density function is known. Work can also be calculated from integrating a force function, or when counteracting the force of gravity, as in a pumping problem. Definite integrals can also be used to calculate the force exerted on an object submerged in a liquid.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/02%3A_Applications_of_Integration/2.05%3A_WorkThis section focuses on calculating the work done by a force over a distance using integration. It explains the concept of work in physics, describes the basic formula W=∫ F(x)dx, and provides exam...This section focuses on calculating the work done by a force over a distance using integration. It explains the concept of work in physics, describes the basic formula W=∫ F(x)dx, and provides examples of varying forces, such as springs and gravitational forces. The section includes applications of integration to solve real-world problems related to work, highlighting how to set up and evaluate integrals in different scenarios.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/06%3A_Applications_of_Integration/6.04%3A_WorkThis section focuses on calculating the work done by a force over a distance using integration. It explains the concept of work in physics, describes the basic formula W=∫ F(x)dx, and provides exam...This section focuses on calculating the work done by a force over a distance using integration. It explains the concept of work in physics, describes the basic formula W=∫ F(x)dx, and provides examples of varying forces, such as springs and gravitational forces. The section includes applications of integration to solve real-world problems related to work, highlighting how to set up and evaluate integrals in different scenarios.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_373%3A_Trigonometry_for_Calculus/08%3A_Non-Right_Triangle_Trigonometry/8.05%3A_Vectors_-_An_Algebraic_ApproachThis section covers vectors from an algebraic perspective, including expressing vectors in coordinate form, converting between geometric and coordinate forms, and performing vector operations such as ...This section covers vectors from an algebraic perspective, including expressing vectors in coordinate form, converting between geometric and coordinate forms, and performing vector operations such as scalar multiplication and addition. It introduces unit vectors, discusses their significance, and explores their use in practical applications like force and equilibrium problems. The section includes examples and exercises to reinforce understanding of algebraic vector manipulation.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/01%3A_Applications_of_Integration/1.06%3A_WorkThis section focuses on calculating the work done by a force over a distance using integration. It explains the concept of work in physics, describes the basic formula W=∫ F(x)dx, and provides exam...This section focuses on calculating the work done by a force over a distance using integration. It explains the concept of work in physics, describes the basic formula W=∫ F(x)dx, and provides examples of varying forces, such as springs and gravitational forces. The section includes applications of integration to solve real-world problems related to work, highlighting how to set up and evaluate integrals in different scenarios.
