It deals with quantities which continuously vary. It can be understood by this example — if there exists a function f x possessing an independent variable x, then in case x is increased with a small amount which would be delta x. Then, the same change will be reflected in the function too as delta f. Integration is just the opposite of differentiation, and therefore is also termed as anti-differentiation.
It is able to determine the function provided its derivative. It measures the area under the function between limits. The process of integration is the infinite summation of the product of a function x which is f x and a very small delta x.
In context to a curve, it provides the total area under the curve from the x axis to the curve from a specific range.
If the specific interval is mentioned then it is known as definite integral otherwise indefinite integral. As integration and differentiation are just the inverse of each other, the integration may provide the original function if derivative is known.
The distance traveled by the function is the area under the curve. This area is calculated using the algebraic expression Integration. It obtains the desired result using addition. One of the main differences between differentiation and integration is that the two algebraic applications are the direct opposite of each other in their application. It is very important to understand the concept and difference of both of them in order to obtain the results of the functions and in order to know where to apply which algebraic expressions.
It is also important to understand the two calculus concepts as they are broadly used in various disciplines like business applications, economics applications, and engineering.
Basically, differentiation is used to calculate the gradient of a curve and it is used to find out the instant rates of change from one point to another whereas Integration is used to calculate the area under or between the curves. Comparison Table Between Differentiation and Integration. What is Differentiation? What is Integration? Main Differences Between Differentiation and Integration. Differentiation is used to calculate the gradient of a curve.
Difference Between Similar Terms and Objects. MLA 8 Morgan, Jecinta. Name required. Email required. Please note: comment moderation is enabled and may delay your comment.
There is no need to resubmit your comment. Notify me of followup comments via e-mail. Written by : Jecinta Morgan. Grayson, and Amy L. The fractional calculus theory and applications of differentiation and integration to arbitrary order.
Elsevier, User assumes all risk of use, damage, or injury. You agree that we have no liability for any damages. What is Differentiation? What is Integration? Difference Between Differentiation and Integration 1 Purpose and Functions of Differentiation and Integration Integration and differentiation can be primarily be differentiated in the way the two concepts are applied and their ultimate results.
Integration One of the principal variations between differentiation and integration is that the two calculus functions are directly opposite of one another in their application. Students and other scholars should focus on understanding one of the concepts after which they will be required to perform the opposite to determine the results of the other function.
Understanding differences that exist between integration and differentiation are essential because it will help individuals to use the right algebraic expression where necessary.
Lastly, it is vital to master the two calculus concepts in basic mathematics because they have consistently been used in various disciplines like economics, business, and engineering. Author Recent Posts. Jecinta Morgan.
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