NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.1 Application of Integrals - PDF Download

NCERT Solutions for class 12 maths chapter 8 exercise 8.1 Application of Integrals deals with the topic that is the area under simple curves. Students should be familiar with curves like circles, parabolas, and ellipses as well as the formulas for the associated standard equations. They should also gain a comprehension of definite integrals. In order to solve the questions in ex 8.1 class 12 maths chapter 8, you need to focus on the diagrams. eSaral’s subject experts of mathematics have provided a clear understanding of the area under simple curves in an easy way.

There are 4 questions in ex 8.1 class 12 maths ch 8 that delivers a good understanding of the concepts using different types of questions. You will be able to solve ex 8.1 by using the concepts explained by the expert faculties of eSaral. These NCERT solutions are also made available here in free PDF format. You can download the PDF from the website of eSaral and start practicing the questions to score good marks in exams. 

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Topics Covered in Exercise 8.1 Class 12 Mathematics Questions

NCERT solutions class 12 maths chapter 8 exercise 8.1 covers an important topic of area under simple curves.

1. Area under Simple Curves

Here, you will learn the easy and intuitive way of finding the area bounded by the curve y = f(x), x-axis and the ordinates x = a and x = b. To find the curve area using integration is an arbitrary strip of height y and width dx. This area is called the elementary area which is located at an arbitrary position within the region which is specified by some value of x between a and b. 

• The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) is given by the formula: Area = $\int_a^b y d x=\int_a^b f(x) d x$ . 
• The area of the region bounded by the curve x = (y), y-axis and the lines y = c, y = d is given by the formula: Area = $\int_c^d x d y=\int_c^d \phi(y) d y$ . 
  

Tips for Solving Exercise 8.1 Class 12 Chapter 8 Application of Integrals

NCERT solutions for ex 8.1 class 12 maths chapter 8 defines the area under curves. To solve questions related to this concept, you must follow the useful tips provided by subject experts of eSaral.

1. In order to solve questions in ex 8.1 class 12 maths associated with finding the area of circle, parabola and ellipse, you must use your mathematical skills to solve the question with an easy method.
2. To solve questions of exercise 8.1, you must understand how to draw the diagram of the question and apply the formula of curve accordingly.
3.  You should also comprehend the concept of curves and their formulas to avoid the errors while solving questions.
   

Importance of Solving Ex 8.1 class 12 Maths chapter 8 Application of Integrals

NCERT solutions for class 12 maths chapter 8 ex 8.1 play an important role in board exams. There are many benefits of solving this exercise. Here, we have provided some of the main benefits which can be checked below.

1. Ex 8.1 class 12 maths ch 8 NCERT solutions have described the concepts of finding the area of some simple curves in easy to understand language that is essential for solving questions of ex 8.1.
2. For solving questions in NCERT solution for ex 8.1, our expert teachers of maths have also explained the formulas of bounded by different curves to solve the questions asked in exams.
3. eSaral’s subject experts have solved all the questions from basic to advanced questions in step by step method in NCERT solutions for class 12 maths chapter 8 ex 8.1 for you to prepare for exams without any doubt.
4. These solutions are also provided in free PDF format for students to cross check their answers.
5. By Solving questions in NCERT solutions will help you score high marks in exams.

Frequently Asked Questions

Question 1. What is the area under the curve?

Answer 1. The region bounded by the curve, the bounded point and the axis is called the area under the curve. With the help of the integration formula and coordinate axis, the area under the curve can be determined.

Question 2. Is it important to solve the examples given before the exercise 8.1 for class 12 maths chapter 8?

Answer 2. Yes, it is very important to solve the examples given before the exercise 8.1 as they include questions which are based on the concepts and formulas related to curve area explained in NCERT solutions class 12 maths chapter 8.