Differentiation vs. Integration — What's the Difference?
By Tayyaba Rehman — Updated on October 30, 2023
Differentiation is the process of finding a function's rate of change, while integration is the process of finding the area under a curve or the accumulated sum.
Difference Between Differentiation and Integration
Table of Contents
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Key Differences
Differentiation is the act of determining the derivative of a function. Integration involves finding the integral, or the antiderivative, of a function.
Differentiation is used to analyze rates of change. Integration is used to compute areas, volumes, and the total accumulation of quantities.
Differentiation breaks down functions into rates. Integration combines values to find total sums or areas.
Differentiation is applied in physics for velocity and acceleration. Integration is used in calculating distances traveled and areas under curves.
The Fundamental Theorem of Calculus connects differentiation and integration, showing they are inverse processes.
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Comparison Chart
Mathematical Process
Finding the derivative
Finding the integral
Purpose
Analyzing rates of change
Computing areas, volumes
Conceptual Basis
Breaking down into rates
Combining values
Applications
Used in physics for motion
Used in calculating areas
Fundamental Theorem
Inverse of integration
Inverse of differentiation
Compare with Definitions
Differentiation
Differentiation determines a function's rate of change.
Differentiation helped find the velocity.
Integration
Integration involves finding antiderivatives.
Integration was used to determine the original function.
Differentiation
Differentiation is a fundamental tool in calculus.
Differentiation was crucial in solving the problem.
Integration
Integration computes the area under a curve.
Integration gave the total area enclosed.
Differentiation
Differentiation finds the slope of a curve at a point.
We used differentiation to determine the curve's steepness.
Integration
Integration finds the accumulated sum over an interval.
Integration helped calculate the total distance.
Differentiation
Differentiation is used in physics to calculate acceleration.
The car's acceleration was found using differentiation.
Integration
Integration is a key technique in calculus.
Integration was essential in solving the equation.
Differentiation
The act or process of differentiating.
Integration
The act or process of integrating.
Differentiation
The state of becoming differentiated.
Integration
The state of becoming integrated.
Differentiation
(Mathematics) The process of computing a derivative.
Integration
The bringing of people of different racial or ethnic groups into unrestricted and equal association, as in society or an organization; desegregation.
Differentiation
(Biology) The process by which cells or tissues undergo a change toward a more specialized form or function, especially during embryonic development.
Integration
(Psychology) The organization of the psychological or social traits and tendencies of a personality into a harmonious whole.
Differentiation
The act or process of differentiating (generally, without a specialized sense).
Integration
(Mathematics) The process of computing an integral; the inverse of differentiation.
Differentiation
The act of treating one thing as distinct from another, or of creating such a distinction; of separating a class of things into categories; of describing a thing by illustrating how it is different from something else.
Integration
(Electronics) The process of placing more than one integrated circuit on a single microchip.
Differentiation
The process of developing distinct components.
Integration
The act or process of making whole or entire.
Differentiation
(geology) The process of separation of cooling magma into various rock types.
Integration
The process of combining with compatible elements in order to incorporate them.
Differentiation
The process of applying the derivative operator to a function; of calculating a function's derivative.
Integration
(society) The process of fitting into a community, notably applied to minorities.
Integration into the city
Differentiation
The act of differentiating.
Further investigation of the Sanskrit may lead to differentiation of the meaning of such of these roots as are real roots.
Integration
(US) racial integration.
Differentiation
The act of distinguishing or describing a thing, by giving its different, or specific difference; exact definition or determination.
Integration
(calculus) The operation of finding the integral of a function.
Differentiation
The gradual formation or production of organs or parts by a process of evolution or development, as when the seed develops the root and the stem, the initial stem develops the leaf, branches, and flower buds; or in animal life, when the germ evolves the digestive and other organs and members, or when the animals as they advance in organization acquire special organs for specific purposes.
Integration
(biology) In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in species' development.
Differentiation
The supposed act or tendency in being of every kind, whether organic or inorganic, to assume or produce a more complex structure or functions.
Integration
The act or process of making whole or entire.
Differentiation
A discrimination between things as different and distinct;
It is necessary to make a distinction between love and infatuation
Integration
The operation of finding the primitive function which has a given function for its differential coefficient. See Integral.
Differentiation
The mathematical process of obtaining the derivative of a function
Integration
In the theory of evolution: The process by which the manifold is compacted into the relatively simple and permanent. It is supposed to alternate with differentiation as an agent in development.
Differentiation
(biology) the structural adaptation of some body part for a particular function;
Cell differentiation in the developing embryo
Integration
The action of incorporating a racial or religious group into a community
Differentiation
Differentiation involves finding derivatives.
Differentiation yielded the function's derivative.
Integration
The act of combining into an integral whole;
A consolidation of two corporations
After their consolidation the two bills were passed unanimously
The defendants asked for a consolidation of the actions against them
Integration
An operation used in the calculus whereby the integral of a function is determined
Integration
Integration is used to calculate volumes.
We used integration to find the solid's volume.
Common Curiosities
Are differentiation and integration related?
Yes, they are inverse processes as per the Fundamental Theorem of Calculus.
Can integration determine area?
Yes, integration is used to calculate the area under a curve.
What does integration find besides area?
Integration can calculate volumes and accumulated quantities.
What is the derivative in differentiation?
The derivative represents the rate of change of a function.
Can integration be used in economics?
Yes, integration is used in economics for finding total cost and revenue.
What is the purpose of differentiation?
Differentiation finds the rate of change of a function.
Is differentiation used in physics?
Yes, differentiation is widely used in physics for motion analysis.
Are there different methods of differentiation?
Yes, there are various methods, including the chain rule and product rule.
Is differentiation always exact?
Differentiation can be exact, but it can also involve approximations in complex cases.
What are antiderivatives in integration?
Antiderivatives are functions that represent the accumulated sum or area.
Does integration have applications in engineering?
Yes, integration is used in engineering for various calculations, including structural analysis.
Can integration find the total growth over time?
Yes, integration can calculate accumulated growth or change over time.
What does the slope of a curve indicate in differentiation?
It indicates the rate at which the function is changing at that point.
Is integration only for continuous functions?
Integration primarily applies to continuous functions, but there are methods for dealing with discontinuities.
Does differentiation only apply to linear functions?
No, differentiation applies to a wide range of functions, not just linear.
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Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
