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# INTEGRALS

NCERT Solutions for class 12 Chapter 7 Integral is all about the anti-derivative which is also called Integration.

### TERMINOLOGIES OF INTEGRALS

Integration as an inverse method of Differentiation:It is a opposite process of differentiating a function as we are provided a derivative so that we could find the original function.

Geometrical Interpretation of Indefinite Integral:It is basically a geometrical representation of Integration.For Example:It is a graphical representation for Integral.

Properties of indefinite Integral:Here you’ll get every necessary properties of Integrals that will help to solve the further problems.

Differentiation and Integrations’s comparison:Here students will know how different is the differentiation from integration on the basis of properties.

Integration’s Method:Comparing to the last year’s session reduction of traditional method can be found with more properties of integration.

Integrating using Substitution Method:It is a simple method where you will learn how to integrate the problem by substituting a value.

Usage of Trigonometric Identities for Integration: Again there is an entry of Trigonometric Identities such as Sine,Cosine,Secant,Tangent,etc so that you use them while integrating a problem.

Besides this all you will be able to define the definite integrals as it has unique value and it is done by using a limit of a sum. Other terminologies like Fundamental Theorem of Calculus,Area function,First fundamental theorem of the integral calculus,Second fundamental theorem of the integral calculus,Evaluation of Definite Integrals by Substitution and Some Properties of Definite Integrals.

## EXAMPLE SOLUTIONS FROM NCERT SOLUTIONS FOR CLASS 12 MATHS CHAPTER 7 INTEGRALS

1.

Solution:

Let I =

……….(i)

Putting

To change the limits of integration from x to t

when x = 0, t = x2 +1 = 0 +1 = 1

when x =1, t = x2 +1 = 1 +1 = 2

From eq. (i),

=

=

=

=  Ans.

2.

Solution:

Let I =  ……….(i)

Putting

Limits of integration when  and when

From eq. (i),

I =

=(ett)42=(ett)24

Ans.

3.  The value of the integral  is:

(A) 6

(B) 0

(C) 3

(D) 4

Solution: Let I =

4.If  then  is:

(A)

(B)

(C)

(D)

Ans.

=

[Applying Product Rule]

=

=

=

=

=

Therefore, option (B) is correct.

5.Evaluate

Solution:

### #CLEARING OUT THE INTEGRALS.

After knowing about the integrals briefly we provided you the NCERT Solutions. We strongly suggest and encourage the students to go through all the solutions from the PDF File.As they are the most probable questions along with answers. It has reduces time of the students.Understandable PDF File will help them to secure better marks in the NCERT Board Examination.

### #MOTIVATION FOR THE STUDENTS.

We the team of STUDYHUNT kindly request all the students to schedule the time table for the study. It means it will allow you to remain in discipline as well as you can play and enjoy the rest of your time except the scheduled one. By this you will get limited and there will be no chance of wastage of time.This interns, You all will score better marks in your Examinations.