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3:24 39:21 Suggested clip Solving Basic Differential Equations with Integration (Differential YouTubeStart of suggested client of suggested clip Solving Basic Differential Equations with Integration (Differential
Declare a variable u and substitute it into the integral: Differentiate u = 4x + 1 and isolate the x term. This gives you the differential, Du = 4dx. Substitute Du/4 for DX in the integral: Evaluate the integral: Substitute back 4x + 1 for u:
Why do we integrate/differentiate equations in Math (or)Physics ? Differentiation reveals the rate-of-change (or instantaneous rate-of-use) of the original quantity or equation. Integration reveals the cumulative effect of the original quantity or equation.
Application in Physics, Integration is very much needed. For example, to calculate the Center of Mass, Center of Gravity and Mass Moment of Inertia of a sports utility vehicle. To calculate the velocity and trajectory of an object, predict the position of planets, and understand electromagnetism.
The Product Rule enables you to integrate the product of two functions. For example, through a series of mathematical somersaults, you can turn the following equation into a formula that's useful for integrating.
Antiderivative and the Indefinite Integral (F(x)+C)=F(x)+C=f(x)+0=f(x). In this definition, the is called the integral symbol, f(x) is called the integral, x is called the variable of integration, DX is called the differential of the variable x, and C is called the constant of integration.
From geometric applications such as surface area and volume, to physical applications such as mass and work, to growth and decay models, definite integrals are a powerful tool to help us understand and model the world around us.
In Electrical Engineering, Calculus (Integration) is used to determine the exact length of power cable needed to connect two substations, which are miles away from each other. Space flight engineers frequently use calculus when planning for long missions.
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