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NCERT Solutions for Exercise 7.5 Class 12 Maths Chapter 7 Integrals are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for Class 12 Maths chapter 7 exercise 7.5 deals with some of the functions which are not discussed yet in earlier exercises. It includes rational functions and advanced levels of logarithmic functions. If students practice this NCERT book exercise diligently, they can attain a good level of understanding of Integrals. Exercise 7.5 Class 12 Maths questions can be seen verbatim in CBSE board examinations. NCERT solutions for Class 12 Maths chapter 7 exercise 7.5 along with some in text examples is recommended to be solved .
12th class Maths exercise 7.5 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Answer:
Given function
Partial function of this function:
Now, equating the coefficients of x and constant term, we obtain
On solving, we get
Given function
The partial function of this function:
Now, equating the coefficients of x and constant term, we obtain
On solving, we get
Given function
Partial function of this function:
.(1)
Now, substituting respectively in equation (1), we get
That implies
Given function
Partial function of this function:
.....(1)
Now, substituting respectively in equation (1), we get
That implies
Given function
Partial function of this function:
...........(1)
Now, substituting respectively in equation (1), we get
That implies
Given function
Integral is not a proper fraction so,
Therefore, on dividing by
, we get
Partial function of this function:
...........(1)
Now, substituting respectively in equation (1), we get
No, substituting in equation (1) we get
Given function
Partial function of this function:
Now, equating the coefficients of and the constant term, we get
and
On solving these equations, we get
From equation (1), we get
Now, consider ,
and we will assume
So,
or
Given function
Partial function of this function:
Now, putting in the above equation, we get
By equating the coefficients of and constant term, we get
then after solving, we get
Therefore,
Given function
can be rewritten as
Partial function of this function:
................(1)
Now, putting in the above equation, we get
By equating the coefficients of and
, we get
then after solving, we get
Therefore,
Given function
can be rewritten as
The partial function of this function:
Equating the coefficients of , we get
Therefore,
Given function
can be rewritten as
The partial function of this function:
Now, substituting the value of respectively in the equation above, we get
Therefore,
Given function
As the given integral is not a proper fraction.
So, we divide by
, we get
can be rewritten as
....................(1)
Now, substituting in equation (1), we get
Therefore,
Given function
can be rewritten as
....................(1)
Now, equating the coefficient of and constant term, we get
,
, and
Solving these equations, we get
Therefore,
Given function
can be rewritten as
Now, equating the coefficient of and constant term, we get
and
,
Solving these equations, we get
Therefore,
Given function
can be rewritten as
The partial fraction of above equation,
Now, equating the coefficient of and constant term, we get
and
and
Solving these equations, we get
Therefore,
[Hint: multiply numerator and denominator by and put
]
Given function
Applying Hint multiplying numerator and denominator by and putting
Putting
can be rewritten as
Partial fraction of above equation,
................(1)
Now, substituting in equation (1), we get
[Hint : Put ]
Given function
Applying the given hint: putting
We get,
Partial fraction of above equation,
................(1)
Now, substituting in equation (1), we get
Back substituting the value of t in the above equation, we get
Given function
We can rewrite it as:
Partial fraction of above equation,
Now, equating the coefficients of and constant term, we get
,
,
,
After solving these equations, we get
Given function
Taking
The partial fraction of above equation,
..............(1)
Now, substituting in equation (1), we get
Given function
So, we multiply numerator and denominator by , to obtain
Now, putting
we get,
Taking
Partial fraction of above equation,
..............(1)
Now, substituting in equation (1), we get
Back substituting the value of t,
Given function
So, applying the hint: Putting
Then
Partial fraction of above equation,
..............(1)
Now, substituting in equation (1), we get
Now, back substituting the value of t,
Given integral
Partial fraction of above equation,
..............(1)
Now, substituting in equation (1), we get
Therefore, the correct answer is B.
Given integral
Partial fraction of above equation,
Now, equating the coefficients of and the constant term, we get
,
,
We have the values,
Therefore, the correct answer is A.
The NCERT Class 12 Maths chapter Integrals covers a total of 12 exercises including one Miscellaneous exercise. Exercise 7.5 Class 12 Maths has a total of 23 main questions along with some few subquestions. In NCERT solutions for Class 12 Maths chapter 7 exercise 7.5 questions difficulty level of questions are of moderate to advanced level which is useful for competitive exams like NEET and JEE Main.
Also Read| Integrals Class 12 Notes
Happy learning!!!
Integration can be used to calculate the centre of gravity, centre of mass etc. which further helps in understanding dynamics of force, pressure etc. in real life.
Integration of cos x is sin x + c
In Board exams, questions of around 20 marks are asked directly which can be of great help to students to score well in the examination.
This exercise caters to questions of higher difficulty level. Hence it can be said that easy questions are not asked from this exercise.
Topics which are related to finding out integrals of rational functions are included in this exercise.
There are 23 main questions in this exercise along with a few subquestions.
You can use them people also used problem
Hi,
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hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
Hello student,
If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
Remember
, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.
I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.
Good luck with your studies!
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