NCERT Solutions for Exercise 7.6 Class 12 Maths Chapter 7 - Integrals
In NCERT solutions for Class 12 Maths chapter 7 exercise 7.6 functions like logarithmic, inverse trigonometric functions, exponential functions etc. are discussed in step by step manner. Solutions to exercise 7.6 Class 12 Maths are prepared in a holistic manner by subject matter experts. Hence NCERT solutions for Class 12 Maths chapter 7 exercise 7.6 provided below can be a good source. There is no need to refer to any other book for these topics as the content provided in the NCERT book is more than sufficient for the examination. Practicing from this exercise can help students score well in exams like JEE Main. The NCERT chapter Integrals also has the following exercise for practice.
Integrals Exercise 7.1
Integrals Exercise 7.2
Integrals Exercise 7.3
Integrals Exercise 7.4
Integrals Exercise 7.5
Integrals Exercise 7.7
Integrals Exercise 7.8
Integrals Exercise 7.9
Integrals Exercise 7.10
Integrals Exercise 7.11
Integrals Miscellaneous Exercise
Integrals Class 12 Chapter 7 Exercise: 7.6
Question:1 Integrate the functions
Answer:
Given function is
We will use integrate by parts method
Therefore, the answer is
Question:2 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Therefore, the answer is
Question:3 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Again use integration by parts in
Put this value in our equation
we will get,
Therefore, answer is
Question:4 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Therefore, the answer is
Question:5 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Therefore, the answer is
Question:6 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Therefore, the answer is
Question:7 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Now, we need to integrate
Put this value in our equation
Therefore, the answer is
Question:8 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Put this value in our equation
Therefore, the answer is
Question:9 Integrate the functions
Answer:
Given function is
We will use integration by parts method
Now, we need to integrate
Put this value in our equation
Therefore, the answer is
Question:10 Integrate the functions
Answer:
Given function is
we will use integration by parts method
Therefore, answer is
Question:11 Integrate the functions
Answer:
Consider
So, we have then:
After taking as a first function and as second function and integrating by parts, we get
Or,
Question:12 Integrate the functions
Answer:
Consider
So, we have then:
After taking as a first function and as second function and integrating by parts, we get
Question:13 Integrate the functions
Answer:
Consider
So, we have then:
After taking as a first function and as second function and integrating by parts, we get
Question:14 Integrate the functions
Answer:
Consider
So, we have then:
After taking as a first function and as second function and integrating by parts, we get
Question:15 Integrate the functions
Answer:
Consider
So, we have then:
Let us take ....................(1)
Where, and
So,
After taking as a first function and as second function and integrating by parts, we get
....................(2)
After taking as a first function and as second function and integrating by parts, we get
................(3)
Now, using the two equations (2) and (3) in (1) we get,
Question:16 Integrate the functions
Answer:
Let suppose
we know that,
Thus, the solution of the given integral is given by
Question:17 Integrate the functions
Answer:
Let suppose
by rearranging the equation, we get
let
It is known that
therefore the solution of the given integral is
Question:18 Integrate the functions
Answer:
Let
substitute and
let
It is known that
Therefore the solution of the given integral is
Question:19 Integrate the functions
Answer:
It is known that
let
Therefore the required solution of the given above integral is
Question:20 Integrate the functions
Answer:
It is known that
So, By adjusting the given equation, we get
to let
Therefore the required solution of the given integral is
Question:21 Integrate the functions
Answer:
Let
By using integrating by parts, we get
Question:22 Integrate the functions
Answer:
let
Taking as a first function and as a second function, by using by parts method
Question:23 Choose the correct answer
Answer:
the integration can be done ass follows
let
Question:24 Choose the correct answer
Answer:
we know that,
from above integral
let
thus, the solution of the above integral is
More About NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6
The NCERT Class 12 Maths chapter Integrals is enough to have a command on this chapter. Exercise 7.6 Class 12 Maths provided here are step by step solutions and covers theoretical concepts also in the questions. NCERT solutions for Class 12 Maths chapter 7 exercise 7.6 is a one stop solution to score well in the exam.
Also Read| Integrals Class 12 Notes
Benefits of NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6
The Class 12th Maths chapter 7 exercise along with a reference book is sufficient for the good command.
Exercise 7.6 Class 12 Maths is on the similar line to that of exercise 7.5. So it will be easy to crack if one has already done exercise 7.5.
Class 12 Maths chapter 7 exercise 7.6 solutions provides good tricks to use in the exam for fastly solving the questions.
Also see-
NCERT Exemplar Solutions Class 12 Maths Chapter 7
NCERT Solutions for Class 12 Maths Chapter 7
NCERT Solutions Subject Wise
NCERT Solutions Class 12 Chemistry
NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Biology
NCERT Solutions for Class 12 Mathematics
Subject Wise NCERT Exemplar Solutions
NCERT Exemplar Class 12 Maths
NCERT Exemplar Class 12 Physics
NCERT Exemplar Class 12 Chemistry
NCERT Exemplar Class 12 Biology
Happy learning!!!