If you want **Application of Integrals Class 12 NCERT Solutions PDF Free** then read this article. I am going to give you the complete solution of chapter 8 of class 12 NCERT in one pdf, apart from this we will deeply understand all the topics and exercises present inside this pdf through today’s article.

First, we know which topics are going to be inside this PDF and all these topics have solutions for *Application of Integrals Class 12* which you will find in the PDF.

- Exercise 8.1
- Exercise 8.2
- Miscellaneous Exercise

Dear students, you just have to read 3 exercises in **Application of Integrals Class 12 **to go above. This is the least exercised chapter of class 12 and very easy questions are also asked from this chapter in your board exams.

Topic | Sub-Topic(s) |
---|---|

Area Under Simple Curves | Finding the area of the region bounded by a curve and x-axis using integration |

Area Between Two Curves | Finding the area of the region between two curves using integration |

Differential Equations | Formulating and solving differential equations using integration |

Application of Integrals in Physics | Finding displacement, velocity, and acceleration using integration |

Application of Integrals in Economics | Finding total revenue, total cost, and profit using integration |

Application of Integrals in Probability | Finding probability density function and cumulative distribution using integration |

Application of Integrals in Geometry | Finding volume and surface area of solids of revolution using integration |

## Get ‘Application of Integrals Class 12 NCERT Solutions PDF’

Class 12 Mathematics is an important stage for students who aspire to pursue higher education in the field of Science, Engineering or Mathematics. One of the important topics in Class 12 Mathematics is the ‘Application of Integrals’.

It is a vast topic that deals with finding areas, and volumes, and solving differential equations using integration. NCERT Solutions for Class 12 Mathematics Applications of Integrals is an important study material for students to score good marks in their board exams.

- Application of Integrals Class 12 NCERT Solutions PDF is an important study material for students studying Mathematics in Class 12.
- It covers a wide range of subtopics, including finding areas, and volumes, and solving differential equations using integration.
- The solutions are designed in a comprehensive and easy-to-understand manner, making it easier for students to grasp the concepts.
- The PDF is easily accessible and can be get from here NCERT Math Solutions websites and the official NCERT website.
- Studying from the NCERT Solutions for Class 12 Mathematics Application of Integrals PDF can help students score good marks in their board exams.

Here are some of the important topics covered in the **Application of Integrals Class 12 NCERT Solutions PDF:**

**Area Under Simple Curves**

Finding the area of a region bounded by a curve and x-axis using integration is one of the important subtopics covered in the Application of Integrals Class 12 NCERT Solutions. Students will learn to find the area of various shapes like triangles, rectangles, circles, and other curves.

**Differential Equations**

Formulating and solving differential equations using integration is another important subtopic covered in the Application of Integrals Class 12 NCERT Solutions. Students will learn how to solve first-order and second-order differential equations using integration and initial conditions.

**Application of Integrals in Physics**

Finding displacement, velocity, and acceleration using integration is an important subtopic covered in the Application of Integrals Class 12 NCERT Solutions. Students will learn how to find the displacement, velocity, and acceleration of a particle in motion using integration.

**Application of Integrals in Economics**

Finding total revenue, total cost, and profit using integration is another important subtopic covered in the Application of Integrals Class 12 NCERT Solutions. Students will learn how to find the total revenue, total cost, and profit of a business using integration.

**Application of Integrals in Probability**

Finding probability density function and cumulative distribution using integration is an important subtopic covered in the Application of Integrals Class 12 NCERT Solutions. Students will learn how to find the probability density function and cumulative distribution of a random variable using integration.

**Application of Integrals in Geometry**

Finding the volume and surface area of solids of revolution using integration is an important subtopic covered in the Application of Integrals Class 12 NCERT Solutions. Students will learn how to find the volume and surface area of various solids like cones, spheres, cylinders, and other shapes.

NCERT Solutions for Class 12 Mathematics Applications of Integrals is an important study material for students to score good marks in their board exams. It covers a wide range of subtopics that will help students understand the concepts clearly. Students can download the Applications of Integrals Class 12 NCERT Solutions PDF from the official NCERT website or from various educational websites.

## Application of Integrals Class 12 Notes PDF

Class 12 Mathematics is a crucial stage for students who aspire to pursue higher education in Science, Engineering, or Mathematics. The topic of ‘Application of Integrals’ is an important part of Class 12 Mathematics that deals with finding areas, and volumes, and solving differential equations using integration.

To score good marks in board exams, it is essential for students to have comprehensive study material that covers all the subtopics of the Application of Integrals. The Application of Integrals Class 12 Notes PDF is one such study material that can prove to be helpful for students.

Here are some of the benefits of studying from the Application of Integrals Class 12 Notes PDF:

**Comprehensive Coverage of Subtopics:**The PDF covers a wide range of subtopics that are important for students to understand. These subtopics include finding the area under simple curves, differential equations, and the application of integrals in physics, economics, probability, and geometry.**Easy-to-understand Notes:**The notes in the PDF are designed in a way that is easy to understand for students. The language used in the notes is simple, and the explanations are clear and concise, making it easier for students to comprehend the concepts.**Well-organized PDF:**The PDF is well-organized and structured, making it easier for students to navigate through the notes. It is designed in a way that follows the curriculum and syllabus of Class 12 Mathematics.**Useful for Quick Revision:**The Application of Integrals Class 12 Notes PDF can be used for quick revision before exams. The notes provide a summary of all the important concepts and subtopics covered in the syllabus, helping students to revise quickly and efficiently.**Easily Accessible:**The PDF can be easily accessible from this article and this blog or from the official NCERT website. Students can access the PDF anytime and anywhere, making it a convenient study material for them.

## Application of Integrals Class 12 Formulas: A Complete Guide

Class 12 Mathematics is an important stage for students who aspire to pursue higher education in Science, Engineering, or Mathematics. The topic of ‘Application of Integrals’ is an integral part of Class 12 Mathematics that deals with finding areas, and volumes, and solving differential equations using integration.

To score good marks in board exams, it is essential for students to have a comprehensive understanding of the formulas used in the Application of Integrals. This article aims to provide a comprehensive guide on the formulas used in the Application of Integrals Class 12.

Here are some of the important formulas used in Application of Integrals Class 12:

**Integration by Substitution:**The formula for integration by substitution is**∫f(g(x))g'(x)dx = ∫f(u)du**, where u = g(x).**Integration by Parts:**The formula for integration by parts is**∫u(x)v'(x)dx = u(x)v(x) – ∫v(x)u'(x)dx.**- The area under Simple Curves: The formula for finding the area under a curve between two points ‘a’ and ‘b’ is
**∫a^bf(x)dx.** **Differential Equations:**The formula for solving differential equations is**∫dy/dx dx = ∫f(x)dx.****Volume:**The formula for finding the volume of a solid of revolution is**∫πf^2(x)dx.****Probability:**The formula for finding the probability of an event is**∫f(x)dx**, where f(x) is the probability density function.

These are some of the important formulas used in Application of Integrals Class 12. It is important for students to understand these formulas thoroughly to solve problems related to the application of integrals.

the Application of Integrals Class 12 formulas is an important aspect of the subject that requires a thorough understanding. Students should focus on understanding the formulas and their application in solving problems related to finding areas, and volumes, and solving differential equations using integration. By mastering the formulas, students can score good marks in their board exams and have a strong foundation for pursuing higher education in Science, Engineering, or Mathematics.

## Application of Integrals Class 12 Miscellaneous Exercise

Class 12 Mathematics is an important stage for students who aspire to pursue higher education in Science, Engineering, or Mathematics. The topic of ‘Application of Integrals’ is an integral part of Class 12 Mathematics that deals with finding areas, volumes, and solving differential equations using integration. To score good marks in board exams, it is essential for students to practice various types of questions, including the Miscellaneous Exercise of Application of Integrals Class 12.

The Miscellaneous Exercise of Application of Integrals Class 12 consists of a variety of questions that test students’ understanding and application of the subject. These questions are based on finding areas under curves, solving differential equations, finding volumes of solids of revolution, and many more. Practising these questions can help students to gain confidence and improve their problem-solving skills.

Here are some of the benefits of practising the Miscellaneous Exercise of Application of Integrals Class 12:

- Better Understanding of the Subject: Practicing the Miscellaneous Exercise of Application of Integrals Class 12 can help students to understand the subject better. By solving different types of questions, students can gain a better understanding of the concepts and their application.
- Improved Problem-solving Skills: The Miscellaneous Exercise of Application of Integrals Class 12 consists of a variety of questions that require students to apply different formulas and techniques. By practising these questions, students can improve their problem-solving skills and be better prepared for board exams.
- Preparation for Competitive Exams: Many competitive exams such as JEE, NEET, and NDA include questions on the topic of the Application of Integrals. Practising the Miscellaneous Exercise of Application of Integrals Class 12 can help students to prepare for these exams as well.
- Better Time Management: Practicing the Miscellaneous Exercise of Application of Integrals Class 12 can also help students to manage their time better. By solving questions within a given time limit, students can improve their speed and accuracy, which is essential for scoring good marks in board exams.
- Boost in Confidence: Solving a variety of questions from the Miscellaneous Exercise of Application of Integrals Class 12 can help students to boost their confidence. By being well-prepared, students can approach the board exams with a positive mindset and perform better.

## FAQ Related to Application of Integrals Class 12

When it comes to the topic of Application of Integrals Class 12, students often have several questions in their minds. Understanding the concepts, preparing for board exams, and gaining knowledge about real-world applications are some common concerns among students.

In this context, frequently asked questions (FAQs) related to the Application of Integrals Class 12 can be helpful. By addressing these FAQs, students can gain a better understanding of the topic, prepare well for exams, and clear their doubts.

### Q: What is the Application of Integrals Class 12 all about?

A: The Application of Integrals Class 12 is a topic in Mathematics that deals with finding areas, and volumes, and solving differential equations using integration.

### Q: Why is the Application of Integrals Class 12 important?

A: The Application of Integrals in Class 12 is an essential topic for students who want to pursue higher education in Science, Engineering, or Mathematics. It also helps in understanding the real-world applications of Mathematics

### Q: How can I prepare for Application of Integrals Class 12?

A: Students can prepare for the Application of Integrals Class 12 by understanding the concepts, practising different types of questions, and solving the Miscellaneous Exercise. They can also refer to NCERT solutions, textbooks, and online resources for better understanding.

### Q: Which formula is used in applications of integrals?

There are several formulas used in the applications of integrals, depending on the specific problem being solved. Some of the commonly used formulas in the topic of Application of Integrals in Class 12 include the Fundamental Theorem of Calculus, integration by substitution, integration by parts, partial fractions, trigonometric substitution, and others. The choice of the formula depends on the type of problem and the specific technique that is best suited to solve it. Students are advised to practice a variety of problems and techniques to gain proficiency in the applications of integrals.

### Q: How many exercises are in Application of integration?

A: In the NCERT textbook for Class 12 Mathematics, **there are a total of three exercises** on the topic of Application of Integrals. These exercises cover a range of topics such as finding areas, and volumes and solving differential equations using integration. In addition to the exercises, there are also miscellaneous examples and additional questions provided to help students gain a better understanding of the topic. It is recommended that students practice a variety of problems from these exercises to gain proficiency in the applications of integrals.

## Conclusion

The Application of Integrals Class 12 is an important topic in Mathematics that has numerous real-world applications. Understanding the concepts and techniques in this topic can help students pursue higher education in Science, Engineering, or Mathematics, as well as gain knowledge about practical applications of Mathematics.

By practising a variety of problems and techniques, students can master the topic and prepare well for board exams and competitive exams. The NCERT textbook for Class 12 Mathematics provides comprehensive coverage of the topic, including exercises, examples, and additional questions.

It is recommended that students refer to this textbook and other study materials to gain a better understanding of the topic and clear their doubts. Overall, the ** ‘Application of Integrals Class 12’** is a fascinating and challenging topic that can provide immense satisfaction to students who are interested in Mathematics.