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NCERT Solutions for Exercise 7.3 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 7.3 is another exercise of the NCERT syllabus chapter integrals. It exposes students to some higher level of problems of integrals which includes complex trigonometric functions. Exercise 7.3 Class 12 Maths can be directly solved by students here only to understand the concepts well. NCERT Solutions for Class 12 Maths chapter 7 exercise 7.3 provided below are holistic in nature and have been prepared by experienced faculties. NCERT solutions for exercise 7.3 Class 12 Maths chapter 7 cannot be neglected to perform better in exams like JEE Main.
12th class Maths exercise 7.3 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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Integrals Class 12 Chapter 7 Exercise: 7.3
Question:1 Find the integrals of the functions
using the trigonometric identity
we can write the given question as
=
Using identity
, therefore the given integral can be written as
Using identity
Again use the same identity mentioned in the first line
The integral can be written as
Let
Now, replace the value of t, we get;
rewrite the integral as follows
Let
......(replace the value of t as
)
Using the formula
we can write the integral as follows
Using identity
we can write the following integral as
=
We know the identities
Using the above relations we can write
The integral is rewritten using trigonometric identities
can be written as follows using trigonometric identities
Therefore,
now using the identity
now using the below two identities
the value
.
the integral of the given function can be written as
Using trigonometric identities we can write the given integral as follows.
We know that,
Using this identity we can rewrite the given integral as
Therefore integration of =
.....................(i)
Let assume
So, that
Now, the equation (i) becomes,
the given question can be rearranged using trigonometric identities
Therefore, the integration of =
...................(i)
Considering only
let
now the final solution is,
now splitting the terms we can write
Therefore, the integration of
The integral of the above equation is
Thus after evaluation, the value of integral is tanx+ c
Let
We can write 1 =
Then, the equation can be written as
put the value of tan = t
So, that
we know that
therefore,
let
Now the given integral can be written as
using the trigonometric identities we can evaluate the following integral as follows
Using the trigonometric identities following integrals can be simplified as follows
The correct option is (A)
On reducing the above integral becomes
The NCERT Class 12 Maths chapter Integrals provided here is of good quality and can be referred by students preparing for various examinations. Exercise 7.3 Class 12 Maths is important for some of the NCERT book Physics topics also. Hence NCERT Solutions for Class 12 Maths chapter 7 exercise 7.3 are good to go for both Maths as well as Physics.
Also Read| Integrals Class 12 Notes
Also see-
Happy learning!!!
Topics like finding out integrals of trigonometric functions, square root functions etc. are asked in the examination.
Integration can be used to find the area, volume etc. in physics and other disciplines.
Yes, it is significant for the board examinations. 5 markers are generally asked from this exercise only.
Moderate level of questions are there in this exercise,
Yes, some functions like sinx, cosx etc. are used in physics calculations. Hence can be referred for Physics topics also.
In total there are 24 questions in this exercise
No, just try to solve maximum and cover maximum concepts. Some questions which are based on the same concepts can be skipped.
No, as NCERT questions are more than sufficient for Boards. You can revise these questions only.
You can use them people also used problem
Hi,
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Since you already have a 12th-grade qualification with 84%, you meet the eligibility criteria and can apply for the Medhavi Scholarship exam. Preparing well for the exam can increase your chances of receiving a higher scholarship.
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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