NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.11) Exercise 7.11

Every child is special  because of their distinctive qualities. They all have areas where they excel and areas where they need to improve. They also have their own learning methods and performance capabilities. Thus, reading the standard NCERT books cannot be the same for all students. This is the reason every student needs a definitive resource that is curated as a match for the NCERT Syllabus. NCERT Solutions provides learning equity. These Solutions can be used by every student to help them according to their requirements. Extramarks has top-quality study materials, prepared by competent faculty members. The solutions by Extramarks have been made simple, accurate, and effective, and are at par with each class level, thereby engaging every student.

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NCERT Solutions Class 11

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Importance of NCERT Solutions for the preparation of Class 12 Examinations:

There are numerous advantages to using NCERT Solutions for board exam preparation. NCERT Solutions for Extramarks are organised in a way that makes them easy to find and use, such as NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11, which has its own page. The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 and other NCERT Solutions aim at making learning easy for students of Class 12, who have to manage multiple subjects all at once. The NCERT Solutions for Class 12 Mathematics are curated by qualified teachers with proper experience. These solutions have been made with the utmost care according to the CBSE Guidelines. Using NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 and other Extramarks resources is like learning from the brilliant minds of the country from the comfort of their personal spaces. Using NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 for doubt-clearance and revision is beneficial.

NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.11) Exercise 7.11 

Exercise 7.11 Maths Class 12 deals with the chapter on Integrals. Students should use Ex 7.11 Class 12 Maths NCERT Solutions to help them make the task of learning and revising the chapter easier. NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 with all the other exercises of the chapter are available for download in one place. The NCERT Solutions Class 12 Maths Chapter 7 Exercise 7.11 are prepared by an expert teacher at Extramarks by following the NCERT (CBSE) book guidelines. NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 contains questions and solutions to the exercise to assist students in revising the entire syllabus and scoring higher in the upcoming exams.

Access the NCERT Solution for Class 12 Maths Chapter 7 – Integrals

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11

Choosing the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 by Extramarks is the go-to option for students. Chapter 7 of Class 12, Integrals, has a lot of exercises for students to deal with. This page provides the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 in PDF format for ease of access. Students should be able to download this via the Extramarks’ website. NCERT Solutions for all the other exercises of the chapter can also be found easily on the website under the same category.

The in-house subject matter experts at Extramarks have diligently researched and put together the reading and learning resources available, such as NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 on the Extramarks’ website. Class 12 students are expected to be thorough with all the subjects in their syllabus and know the solutions to every question. This is why the NCERT Solutions by Extramarks try to be an aid to the preparation of these students. There is a separate category for each subject including Mathematics. The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 along with the exercises of every chapter can be availed from the website. The solutions are easy to comprehend and can be used as a step-by-step guide while solving the exercises of the chapter.

Apart from the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 there are other exercises also important as they contain many important questions. All the questions of the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 are personally solved by qualified faculty members by Extramarks. These NCERT Solutions are of premium quality and are perfect assistance for Class 12 examinations. The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 are important to the revision of every student. The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 has all the concepts and important pointers for understanding the chapter intricately.

The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 help save time and make the learning process simple and quick. The students would not have to waste time if they are confused, they can easily refer to NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 for all their doubts.

Q.1

Show that0af(x)g(x)dx=20af(x)dx, if f and g are defined as f(x)=f(ax) and g(x)+g(ax)=4

Ans

Let  I=0af(x)g(x)dx...(i)   =0af(ax)g(ax)dx          [∵    0af(x)dx=0af(ax)dx]   =0af(x)g(ax)dx  ...(ii)       [f(x)=f(ax)]Adding equation (i) and (ii), we get     2I=0af(x)g(x)dx+0af(x)g(ax)dx      =0af(x){g(x)+g(ax)}dx      =0af(x)(4)dx          [∵  g(x)+g(ax)=4]      I=20af(x)dx          Hence​ proved.

Q.2

Choose the correct answerThe value of π2π2x3+xcosx+tan5x+1dxisA0B2CπD1

Ans

Let   I=π2π2(x3+xcosx+tan5x+1)dx       =π2π2x3dx+π2π2xcosxdx+π2π2tan5xdx+π2π21dxSince, if f(x) is even function then, aaf(x)dx=20af(x)dxand if f(x) is odd function then,   aaf(x)dx=0    I=0+0+0+20π21dx      =2[x]0π2     =2(π2)     =πTherefore, the correct option is C.

Q.3

Choose the correct answerThe value of0π2log4+3sinx4+3cosxdx isA2B34C0D2

Ans

Let  I=0π2log(4+3sinx4+3cosx)dx   ...(i)       =0π2log{4+3sin(π2x)4+3cos(π2x)}dx      =0π2log(4+3cosx4+3sinx)dx...(ii)Adding equation (i) and equation (ii), we get     2I=0π2{log(4+3sinx4+3cosx)+log(4+3cosx4+3sinx)}dx       =0π2{log(4+3sinx4+3cosx×4+3cosx4+3sinx)}dx      =0π2log(1)dx      I=0Therefore, the correction option is C.

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FAQs (Frequently Asked Questions)

1. How many questions are there in the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11?

The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 solutions by Extramarks has all the 21 questions and solutions of Exercise 7.11 Maths Class 12.

2. What are the benefits of having the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11?

The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 can be used as a guide while solving the chapter. The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 can also come in handy during the last-minute preparation and revision before the examination. Class 12 Mathematics can be tough; therefore, it is good to have something like the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 by the student’s side to help them when they are having trouble.This will also help to keep the flow going while working on Exercise 7.11 Math Class 12.

3. How can a student prepare well for the CBSE Class 12th board examination?

The foremost preparatory step that a student needs to take is to study and analyse the syllabus properly. Then devise a plan according to it. Using past years’ papers and study material like the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 can prove to be extremely useful. Getting command over weak areas and continuously revising the strong areas of one’s preparation is also important. Self-assessment by using NCERT Solutions like NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 and other revision material also enhances preparation and, in turn, results.

4. What is in the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11?

The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 contain detailed solutions to the chapter on Integrals. Extramarks makes sure that students gain clear knowledge and achieve higher marks in their forthcoming examinations. The NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 not only have the solutions but also proper steps explaining everything needed by the student. 

5. Are NCERT Solutions beneficial for Class 12 students?

Class 12 is a significant step in a student’s life. Therefore, NCERT Solutions should be a must in their study material for outstanding results. The NCERT Solutions provided are on-point answers and can be used while self-studying as well. Students need to understand their study and learning patterns to constantly improve their expected performance. Using study materials like NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11 will provide an extra edge to the preparations.