Differentiation and Integration with Mathematical expressions and Graphical representation
Differentiation:
Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Math’s, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity.
The following table shows the differentiation rules: Constant Rule, Power Rule, Product Rule, Quotient Rule, and Chain Rule. Scroll down the page for examples and solutions on how to use the rules.
Let’s take an example for differentiation and solve it with math equation formulas.
Same equation we can solve with graphical method
Graph for equation before and after differentiation:
We are using Desmos for plotting the graph, below is the URL and screenshot for it. We can find the graph plotted below.
Differentiation
Integration:
The integration denotes the summation of discrete data. The integral is calculated to find the functions which will describe the area, displacement, volume that occurs due to a collection of small data, which cannot be measured singularly.
Let’s take an example for integration and solve it with math equation formulas.
Now, Let’s put values and solve the equation (Assume limits from 5 to 10):
According to the Fundamental Theorem of Calculus,
So, just evaluate the integral at the endpoints.
Taking first limit and calculating.
f (5) = 5 (5+5) = 50
Taking second limit and calculating.
f (10) = 10(10+5) = 150
We can now solve using the Graphical method.
Integration_New
Trigonometric formulas for Differentiation and Integration:
Let’s look at the comparison between Differentiation and Integration:
Differentiation and Integration are the two major ideas of calculus. Differentiation is employed to review the little modification of a amount with relevance unit modification of another. On the opposite hand, integration is employed to feature tiny and separate knowledge, that can not be value-added singularly and representing in a very single worth.
Conclusion for Differentiation vs. Integration
1) One important variations between differentiation and integration is that the two calculus functions are directly opposite of one another in their application.
2) Understanding variations that exist between integration and differentiation area unit essential as a result of it’ll facilitate people to use the correct pure mathematics expression wherever necessary.
Reference: Desmos
