difference between integration and differentiation
Answers
Answer:
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. They are used to arrive at different answers, which is the fundamental difference. Differentiation is used in calculating the gradient of the curve. Nonlinear curves have different slopes at any given point, which makes it difficult to determine their gradients. The algebraic expression used to determine the change incurred from one point to another with a unit is referred to as differentiation. On the other hand, integration is an algebraic expression used in calculating the area under the curve because it is not a perfect shape after which area can easily be calculated.
2) Directly Opposite
Differentiation and Integration algebraic functions are directly opposite of one another, specifically in their application. If one performs integration, he or she is said to be showing the opposite of differentiation while if one performs differentiation, he or she is performing opposite of integration. For example, integration and differentiation form a relationship that is similarly depicted when one performs the square of a number and then finds the square root of the result. Therefore, if one wants to find the opposite of an integrated number, he or she will be required to perform the differentiation of the same number. Simply, integration is the reverse process of differentiation and vice versa.
3) Real Life Application for Differentiation and Integration
In real life scenarios, integration and differentiation have been found to be applied differently to each concept used in providing different results. Nevertheless, it is remarkable to highlight that both differentiation is essential calculus concepts that make life easy. One of the main application of integration is calculating the areas of curved surfaces, calculating the volume of objects, and calculating the central point among other functions.
On the other hand, differentiation concept is significantly used in calculating instantaneous velocity and used in determining whether a function is increasing or decreasing accordingly. This is a clear demonstration of how the two concepts are applied in the lives of individuals.
4) Speed and Function of Differentiation and Integration
The other difference between integration and differentiation is the role they play when it comes to any given function under investigation. According to mathematicians, differentiation significantly helps in determining the speed of the function by helping in the calculation of instantaneous velocity. On the other hand, integration is concerned with determining the distanced travelled by any given function. The area under the curve is estimated to be equivalent to the distance travelled by the function. Integration algebraic expression helps in calculating the area under the curve, which amounts to the distance travelled by the function.
Algebraic Expressions/Formula for Differentiation and Integration
It is also worth noting that differentiation and integration have different algebraic expressions, which are used in the calculation. This explains why the two calculus concepts will always provide different results. The derivative of a function f(x) concerning the variable x and according to the product rule will be defined as:
Difference Between Differentiation and Integration
On the other hand, the integration formula or the integral area under the curve can be calculated by use of the formula:
∫f(x) dx, which is the formula adopted under substitution method.
5) Addition and Division
The other method of comparing integration to differentiation is by specifically explaining how each function realizes its results. Integration determines the outcome of a specific function by adding the aspects associated with calculation. On the other hand, differentiation determines instantaneous velocity and the speed of the function through division.
Answer:
integration = integration is the method to integrate all the values terms,respect to variables in the function by various methods of integration .
differentiation = differentiation is a method to differentiate the function as respect to the variables
integration is nearly opposite to differentiation...