Definite Integral in Hindi | निश्चित समाकलन | lecture notes of definite integral in pdf

Introduction of Definite Integral 

In this article we have discussed basic concept and definition of definite integral. What is difference between indefinite integral and definite integral. this article helpful to CLASS 12 AND POLYTECHNIC students. This is also helpful to IIT JEE /NDA students.

Definite integral is most important topic for class 12,Diploma,IIT JEE and NDA students. Many question asked related to this topic.

in this article i will provide full basic concept of definite integral and Important properties of definite integral .This  article we will discussed following type of question.

1.introduction and definition of definite integral

2.find definite integral by substitution method 

3.find definite integral using partial fraction

4.find definite integral using special function

5.find definite integral using integration by part.
     Remember how to taken First term of Integration: ILATE

  I: inverse function
L: Logarithmic function
A : Algebraic Function
T: Trigonometric Function 
E : Exponential function 

 lecture notes of definite integral in pdf 

Definition of Definite Integration:

जब किसी फलां का समाकलन दिये गए किन्ही  दो निश्चित सीमाओ के  लिए किया जाता है तो उसे निश्चित समाकलन कहते है। 

let F(x) be a integral of the function f(x) defined on [a,b] , then F(b)-F(a) is called the definite integral of f(x) between the limits a and b.

It is defined as 

Definite integral by substitution method 

when substitution is used for definite integral , lower limit and upper limit of the integral also change corresponding new variables.

यदि समाकलन ज्ञात करते समय प्रतिस्थापन करना पड़े तो निश्चित समाकलन की सीमाओ को भी प्रतिस्थापन की चर  राशि के अनुसार परिवर्तित करना पड़ता है :

Note:

Substitution Method मे हमे हमेसा यह ध्यान रखना होता है की किस फलन का अवकलन दिया है । जिस फलन का अवकलन दिया होता है उस फलन को हम t मानकर  question को हल करते है|   f(x)=t   , f'(x) dx=dt.

  solve of the following problem:

1. ∫e^x cos (e^x) dx with limit 0 to 1.

2.∫ (tan^-1x)²/(1+x²) dx with limit 0 to 1

3. ∫ x sin^-1x /(1-x²)^1/2dx with limit 0 to 1

4. ∫sin (tan-1x)/ (1+x2) dx with limit 0 to ∞

 

Evaluate ∫1/(a²cos²x+ b²sin²x) dx with limit 0 to π/2

evaluate ∫ 1/(5+4cosx) dx with limit 0 to π

evaluate ∫ 1/(4+5sinx) dx with limit 0 to π/2

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