Class 12 Maths NCERT solutions of Exercise 7.4-Integrals

Class 12 Maths NCERT solutions of Exercise 7.4 of chapter 7-Integrals are created by an expert teacher of maths. These NCERT solutions are the solutions to the unsolved questions of class 12 maths exercise 7.4 of chapter 7-Integrals of the NCERT textbook prescribed by the CBSE School board of India.NCERT solutions of exercise 7.4 will help in your preparation of the board exam of CBSE and in clearing the ways of methods of integration used in different kinds of functions. By studying these NCERT Solutions you will become capable to solve all problems related to the integration.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

In solving unsolved questions of exercise 7.4 of chapter 7-Integrals you have to understand solutions of algebraic expressions so you can revise the maths chapter of previous classes like quadratic equations. Click here to revise complete square of polynomial

 

Class 12 Maths NCERT solutions of Chapter 7 Integrals

Exercise 7.1- Integrals

Exercise 7.2-Integral

Exercise 7.3-Integrals

Exercise 7.4 -Integral

 

Class 12 Maths NCERT solutions of Exercise 7.4 of chapter 7-Integrals

Exercise 7.4-Integrals

Integrate the functions in exercises 1 t0 23.

Ans. Integrating the functions

Let t = x³

dt = 3x²dx

Substituting the value dt = 3x²dx and t = x³

Substituting back the value of t = x³

Ans.We are given the function

Integrating it

Let t = 2x

Substituting the value 2x=t and dx=dt/2

Using the formula for integration

Therefore

Substituting back the value of t=2x

Ans. We are given

Let t= 2-x

dx= -dt

Putting value of dx =-dt and 2-x= t in the integral

Applying the integration formula

We have

Substituting back the value of t= 2-x, we get

Ans.

We are given

Integrating it

Let t= 5x

Substituting the value of dx =dt/5 and 5x = t

Applying the integration formula

We have

Substituting back the value of t=5x

Class 12 Maths NCERT solutions of Exercise 7.4 of chapter 7-Integrals

Ans. We are given

Integrating it

Let t= √2x²

Substituting  value of xdx ,we have

Applying the integration formula

We get

Substituting back the value of t=√2 x²

We are given

Integrating the given function

Let t = x³

Substituting the value x²dx = dt/3 and t= x³, we get

Applying the integration formula

Substituting back the value of t = x³

.

Ans.We are given the function

Integrating the function

Solving integration of both fraction separately

Solution of first part

Let t = x² – 1

Substituting the value of xdx = dt/2 and x² – 1 = t

Substituting the value of  t = x² -1

We have

Integration of first part =

Putting this value as the integration of  first part and applying the following  integration formula for solving the second fraction

We have

Ans. We are given

Integrating the function

Let t= x³

3x²dx =dt

Substituting the value of x²dx = dt/3 and x³ = t

Applying the integration formula

 

Substituting back the value of t = x³

Class 12 Maths NCERT solutions of Exercise 7.4 of chapter 7-Integrals

Ans. We are given

Integrating the given function

Let t = tanx

dt = sec²x.dx

Substituting the value of sec²x.dx = dt and tanx=t

Applying the integration formula

Substituting back the value of t=tanx

Ans. We are given

Integrating the given function

Let t = x+1 ,we can rewrite the denominator x² +2x+2= (x+1)² +1

dt = dx

 

Applying the integration formula

Substituting back the value of t = x+1

Ans.We are given the function

Integrating it

Rewriting the denominator of the given function

9x² +6x + 1 +4 = (3x+1)² +2²

Let t = 3x +1

Substituting the value 3x+1=t and dx= dt/3

Applying the integration formula

 

We have

Substituting back the value of t=3x+1

Ans. We are given

Converting the terms of denominator into a complete square form

7 -6x -x² = -(x² +6x -7+3² -3²)= -(x+3)² +16= 4² -(x+3)²

So,we have

Now,integrating the function

Let t= x+3

dt = dx

Substituting the value of dx=dt and x+3= t

Applying the formula of integration

 

Substituting back the value of t = x +3

Class 12 Maths NCERT solutions of Exercise 7.4 of chapter 7-Integrals

Ans. We are given the function

Integrating the given function

Converting the terms of denominator into complete square form

(x-1)(x-2)=x²-3x +2 +(3/2)² -(3/2)²

= (x-3/2)²-(1/2)²

So,we have

Now, integrating it

dt =dx

Substituting x-3/2= t and dx= dt in the integral

Using the integration formula

 

So, we have

Substituting back the value of t = x -3/2, we have

 

Converting the denominator 8 + 3x -x² into the terms of complete square

8 + 3x -x²

 

 

Now, we have

Now,integrating the function

Let t= x -3/2

dt =dx

Substituting the value dx=dt and t= x -3/2

Applying the integration formula

So, we have

 

Substituting back the value of t = x-3/2

Ans. We are given

Converting the terms of denominator into the form of complete square

(x -a)(x-b)  = x² – (a +b)x + ab=x² – (a +b)x + ab +[(a+b)/2]² -[(a+b)/2]²

Integrating it

dx =dt

Substituting the value of   

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals	Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds	Chapter 12- Electricity
Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process	Chapter 14-Sources of Energy
Chapter 7-Control and Coordination	Chapter 15-Environment
Chapter 8- How do organisms reproduce?	Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT Solutions for Class 11 Physics

Chapter 1- Physical World

chapter 3-Motion in a Straight Line

NCERT Solutions for Class 11 Chemistry

Chapter 1-Some basic concepts of chemistry

Chapter 2- Structure of Atom

NCERT Solutions for Class 11 Biology

Chapter 1 -Living World

NCERT solutions for class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution