INTEGRATION (Questions) #trendingshorts #latestvideo #shrots video #successzone

Integration and Differentiation
Differentiation

Differentiation is a branch of calculus that studies the rate at which a quantity changes with respect to another quantity. It is used to find the slope of a curve at any point and to determine instantaneous rates of change.

Definition

If y=f(x), then the derivative of y with respect to x is written as:

dx
dy
​

=f
′
(x)

Applications
Finding velocity from displacement.
Calculating acceleration from velocity.
Determining the slope of curves.
Solving optimization problems (maximum and minimum values).
Example

If y=x
2
, then:

dx
d
​

(x
2
)=2x

Integration

Integration is the reverse process of differentiation. It is used to find the original function when its derivative is known and to calculate areas under curves.

Definition

The integral of a function f(x) with respect to x is written as:

∫f(x)dx=F(x)+C

where C is the constant of integration.

Applications
Finding displacement from velocity.
Calculating area under a curve.
Determining volumes of solids.
Solving problems in physics, engineering, and economics.
Example

For f(x)=2x:

∫2xdx=x
2
+C
Relationship Between Integration and Differentiation

Integration and differentiation are inverse processes.

dx
d
​

(∫f(x)dx)=f(x)

and

∫
dx
d
​

[f(x)]dx=f(x)+C

This relationship is known as the Fundamental Theorem of Calculus.

Summary
Differentiation finds the rate of change of a function.
Integration finds the original function or the area under a curve.
They are inverse operations and form the foundation of calculus.

***About Success Zone ***
Success zone: The Art Of making People
Take the opportunity to introduce our mission as "Success Zone" to the student who is aspiring for the engineering and medical entrance examination. Serious aspirants with honest endeavors can only succeed in this fierce competition.
Specific about "Success Zone" is that here everyone helps the student to analyze themselves and make them realize their potential. We believe that each student has something special that can be built upon.

For more info contact us:
Contact number: 9304606280, 9708168945, 9835161763, 06546-359670
Website: https://www.successzon.com/
Facebook: https://www.facebook.com/successzon
Instagram: https://www.instagram.com/zonesuccess/
Post your doubts here: https://www.successzon.com/
Technical Partner: Softication Technology (https://www.softication.com/)

#ncertmaths #ncertbooks #ncertsolution #ncertsummary #ncertatyourfingertips #ncertapp #ncertartandculture #sets #relations #functions #setsambalpur #setsaree #setsclass11 #setsclass11iitjee #setsclass11maths

Видео INTEGRATION (Questions) #trendingshorts #latestvideo #shrots video #successzone канала Success Zone Hazaribagh