Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 12 Mathematics II 7. Integrals to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 12 Mathematics II 7. Integrals to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 7.6. Whether you are studying for board exams or mid-term exams, 12 Mathematics II Chapter 7. Integrals solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise 7.6
Integrate the functions in Exercises 1 to 22.
Ques.1. 
Ans. 
= 
[By product rule]
= 
= 
= 
= 
Ques.2. 
Ans. 
= 
[By product rule]
= 
= 
= 
= 
Ques.3. 
Ans. 
= 
[By product rule]
= 
= 
= 
[Again By product rule]
= 
= 
= 
= 
= 
Ques.4. 
Ans. 
= 
= 
[By product rule]
= 
= 
= 
= 
Ques.5. 
Ans. 
= 
= 
[By product rule]
= 
= 
= 
= 
Ques.6. 
Ans. 
= 
= 
[BY product rule]
= 
= 
= 
= 
Ques.7. 
Ans. Let I = 
Putting 
I = 
= 
= 
= 
[Integrating by parts]
= 
= 
= 
= 
= 
Ques.8. 
Ans. Let I = 
= 
= 
= 
= 
= 
= 
= 
Ques.9. 
Ans. Let I = 
……….(i)
Putting 
From eq. (i),
I = 
= 
= 
[Applying product rule]
= 
= 
= 
= 
Putting 
and 
= 
= 
Ques.10. 
Ans. Putting
= 
= 
[By product rule]
= 
= 
[Again By product rule]
= 
= 
= 
Ques.11. 
Ans. Let I = 
……….(i)
Putting
From eq. (i),
I = 
= 
= 
= 
[By product rule]
= 
= 
= 
= 
= 
Ques.12. 
Ans. 
= 
[By product rule]
= 
= 
= 
= 
Ques.13. 
Ans. Let I = 
= 
= 
= 
=
= 
Ques.14. 
Ans. 
= 
= 
= 
= 
= 
= 
= 
= 
Ques.15. 
Ans. 
= 
= 
[By product rule]
= 
= 
= 
= 
Ques.16. 
Ans. Let I = 
It is in the form of 
since,
here 
and 
I = 
Ques.17. 
Ans. Let I = 
= 
= 
I = 
It is in the form of since,
here 
and 
I = 
Ques.18. 
Ans. Let I = 
= 
= 
= 
= 
It is in the form of since,
here 
and 
= 
Ans. Let I = 
It is in the form of since,
here 
and 
I = 
= 
Ans. Let I = 
= 
= 
I = 
It is in the form of since,
here 
and 
= 
= 
.
I = 
Ans. Let I = 
= 
[By product rule]
I = 
I = 
[Again By product rule]
I = 
= 
5I = 
I = 
Ans. Putting 
= 
= 
= 
= 
= 
[By product rule]
= 
= 
= 
= 
= 
Ques.23. 
equals to
(A) 
(B) 
(C) 
(D) 
Ans. Let I =
= 
……….(i)
Putting 
From eq. (i), I = 
= 
=
hance, option (B) is correct.
equals:(A) 
(B) 
(C) 
(D) 
Ans. Let I =
= 
It is in the form of since,
here 
and 
I = 
hance, option (B) is correct.
Exercise 7.6 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 12 Mathematics II Chapter 7. Integrals solutions help you understand the core concepts and practice effectively.
Revision is the key to exam success. Our notes for 12 Mathematics II highlight important formulas, key definitions, and exam-ready points from Chapter 7. Integrals. These quick revision notes make last-minute preparation easy.
Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 7.6 include complete solutions for 12 Mathematics II Chapter 7. Integrals exercises. With step-by-step answers, you gain clarity and confidence to attempt similar exam questions.
To boost your preparation, we also provide additional important questions with answers. These are prepared from previous year board papers, sample papers, and important concepts of Chapter 7. Integrals. Practicing these ensures you are well-prepared for both board and mid-term exams.
Our Exercise 7.6 are useful for both board exams and mid-term exams. For 12 Mathematics II, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 7.6 for 12 Mathematics II Chapter 7. Integrals are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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