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NCERT Solutions for Class 12 Maths Exercise 8.1 Application Of Integrals: Chapter 8 of class 12 Maths, Application Of Integrals is a very important chapter. The chapter is helpful for the students who are preparing for the competitive exams like JEE and NEET. There are a total of 13 questions that includes short-form, long-form and MCQ in the exercise 8.1. Top subject experts have designed the ex 8.1 class 12 solutions for the students.
Students have to carefully go through the chapter and solve the in-text questions that are provided at the end of each chapter. This will allow them to get a clear idea on the chapter. The NCERT class 12 Maths solutions comes with the step by step guidance on how to go about a problem. Before getting in to other reference books, be thorough with the NCERT solutions. Read along the article to find out more!
Students can check the important topics or the exercise topics for clear understanding on the chapter in the table given below:
| Sr. No | Topic Name |
|---|---|
| 8.1 | Area under the curves |
| 8.2 | The area of the region bounded by a curve and a line |
| 8.3 | Area between two curves |
There are two important formulas for the students to remember and to be thorough with. This is because, most of the questions that are asked in the exam can be tackled with these formulas:
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
Other than chapter 8, here are the direct links to the articles that consist of all the details of all chapters of class 12. Students can refer to them from the links given below:
Q.1. How many questions does NCERT Application on Integrals include?
Ans: NCERT Class 12 chapter 8 includes exercise 8.1 with 13 questions, exercise 8.2 with 7 questions and miscellaneous exercise with 19 questions.
Q.2. Why should I refer to Embibe’s ex 8.1 Class 12 solutions?
Ans: Students should refer to Embibe’s ex 8.1 Class 12 Maths NCERT solutions because they are designed by academic experts and provide the latest and updated information to students. Every question is supplemented by step-by-step solutions to help students answer questions in the best possible way.
Q.3. Where can I get Maths exercise 8.1 Class 12 solutions online?
Ans: Students can get ex 8.1 Class 12 Maths NCERT solutions online from this article or by visiting the website of Embibe.
Q.4. What are the important topics in NCERT Class 12 Maths Chapter 8?
Ans: In Class 12 Maths Chapter 8, students learn about applications of integrals and how to use them to calculate the area under the curves, the area of a region bounded by curves, and a line area between two curves.
Q.5. What is the type of questions in ex 8.1 Class 12?
Ans: Exercise 8.1 Class 12 Maths contains 13 questions, 11 long and 2 MCQ based questions.
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