Exams Chapter Solutions NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise

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Last Modified 25-10-2024

NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Miscellaneous Exercise: Chapter 8 class 12 deals with the most important topic, Application of Integrals. The topic is not just useful for the board exams but also for all the competitive exams. There are many complex formulas that could be used for the competitive exams like JEE and NEET. This is why we have provided the Class 12 Maths Chapter 8 Miscellaneous Exercise Solutions in accordance with the CBSE board’s marking structure and exam pattern.

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These Maths NCERT Solutions Class 12 PDFs for Chapter 8 can be downloaded and used offline by students from the official website. NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise and a variety of study tools, including PDFs of NCERT books, solution sets, and previous year’s question papers, may be found on the Embibe website for! Read along to find out more!

NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise: Important Topics

Before we go in depth with regard to the topic, let us see an overview on the class 12 chapter 8 important topics:

8.1	Introduction
8.2	Area under the curves
8.2.1	The area of the region bounded by a curve and a line
8.3	Area between two curves

NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise: Points To Remember

Let’s take a look at the important points to remember for class 12 chapter 8:

Formula to find the Area under Simple Curves:

(i) The area of the region bounded by the curve y=f(x)y=fx, xx-axis, and the lines x=ax=a and x=bx=b (b>a)b>a is given by the formula: Area =∫baydx=∫baf(x)dx=∫abydx=∫abfxdx.

(ii) The area of the region bounded by the curve x=ϕ(y)x=ϕ(y), yy-axis, and the lines y=c, y=dy=c, y=d is given by the formula:

Area=∫dcxdy=∫dcϕ(y)dy=∫cdxdy=∫cdϕydy.

2. Formula to find the Area between Two Curves:

(i) The area of the region enclosed between two curves y=f(x)y=fx, y=g(x)y=gx, and the lines x=a,x=bx=a,x=b is given by the formula, Area =∫ba[f(x)−g(x)]dx Area =∫abfx-gxdx, where f(x)≥g(x)f(x)≥g(x) in [a, b][a, b].

(ii) If f(x)≥g(x)f(x)≥g(x) in [a, c][a, c], and f(x)≤g(x)f(x)≤g(x) in [c, b], a<c<b[c, b], a<c<b, then Area =∫ca[f(x)−g(x)]dx+∫bc[g(x)−f(x)]dx

NCERT Solutions for Class 12 Maths: All Chapters

Here are the NCERT Class 12 detailed solutions of other chapters:

FAQs on NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise

Q.1: What is the best website for NCERT Solutions of Class 12 Maths Chapter 8?
Ans: Students can find the solutions for miscellaneous exercises in chapter 8 class 12 maths from the official website.

Q.2: Is Maths Chapter 8 challenging?
Ans: In Maths, it is essential to understand all the concepts and the students who fail to do that find the subject difficult. To make it easier to understand all the topics the students can go through the whole chapter and try to understand the basics of the topics. If they do that, the chapter 8 is challenging.

Q.3. Are NCERT textbooks enough for the preparation of Class 12 Maths?
Ans: Yes, the NCERT books are enough for the students to get good marks in the board exams. Students just need to make sure that they cover all the topics from the Class 12 Maths syllabus and do not skip any of them.

Q.4: How many important examples are there in Class 12 Maths Chapter 8 Miscellaneous Exercise?
Ans: There are five examples in the Miscellaneous Examples portion of Chapter 8 of Class 12 Maths (from Example 11 to Example 15). These examples can be used to complete the Class 12 Maths Chapter 8 Miscellaneous Exercise in the NCERT textbook.

Q.5: What is the main point of NCERT Class 12 Maths Chapter 8?
Ans: NCERT Class 12 Maths Chapter 8 Application of Integrals’ main idea is to use geometric formulae to calculate the area of various geometric shapes, as well as the area between two curves, the area between two curves and lines, the area between arbitrary positions, and trigonometric identities integrals.