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Hace 4 días · Key Concepts. 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.
- Hooke’s Law
An oscillation is a back and forth motion of an object...
- Hooke’s Law
Key Concepts. The integration-by-parts formula (Equation \ref{IBP}) allows the exchange of one integral for another, possibly easier, integral. Integration by parts applies to both definite and indefinite integrals.
Hace 4 días · Write the triple integral \[\iiint_E f(x,y,z) \,dV\nonumber \] for an arbitrary function \(f\) as an iterated integral. Then evaluate this triple integral with \(f(x,y,z) = 1\). Notice that this gives the volume of a sphere using a triple integral.
Hace 4 días · This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use integration by parts to find the integral of a product of functions.
In this explainer, we will learn how to use integration by parts to find the integral of a product of functions. The fundamental theorem of calculus tells us that differentiation and integration are reverse processes to one other. This means that any rule for differentiation can be applied as an integration rule in reverse.
Hace 4 días · In this explainer, we will learn how to apply integrals to solve problems involving motion in a straight line. As the particle moves in a straight line, its position is described by a single coordinate along the line of motion. By calling this line the 𝑥 -axis, the position of the particle at time 𝑡 is then described by the ...
Hace 2 días · The beta function (also known as Euler's integral of the first kind) is important in calculus and analysis due to its close connection to the gamma function, which is itself a generalization of the factorial function. Many complex integrals can be reduced to expressions involving the beta function.
