NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

NCERT Mathematics textbook solutions also include solved examples that help in visualizing mathematical problems and learning the correct application of formulas. Class 12 Mathematics NCERT Textbook Chapter 8 PDF download option offers convenience for offline study and the miscellaneous exercise solutions strengthen problem-solving skills. Students can also explore NCERT Book Class 12 Maths Chapter 8 important questions to get exam-ready. According to new syllabus given in latest NCERT book for 2025-26, there is only two exercises (including miscellaneous) in chapter 8 of 12th Maths.

Key Features of Application of Integrals NCERT Solutions

Application of Integrals Class 12 NCERT Textbook solutions PDF is designed to make complex concepts easy to understand. It includes detailed solutions for all problems, ensuring students grasp the use of integration to calculate areas under curves. Along with NCERT Textbook solutions to Class 12 Math Book Chapter 8 previous year questions, the PDF also provides a formula sheet that summarizes key mathematical expressions. These resources are essential for tackling tough problems from NCERT Class 12th Mathematics Chapter 8 notes.

NCERT Book Miscellaneous exercises, such as Class 12 Math Chapter 8 miscellaneous exercise solutions, enhance a student’s ability to deal with real-world problems where integral calculations are used. To make learning engaging, students can also refer to NCERT Class 12 Maths Chapter 8 video lectures, which provide a visual approach to solving area-based problems.

How to Prepare Effectively for Chapter 8 NCERT Mathematics

For mastering Application of Integrals NCERT Class 12 Mathematics solutions, students should start by thoroughly studying the textbook and practicing examples provided in NCERT Class 12th Maths Chapter 8 practice questions. Attempting unsolved problems from Class 12 Math Textbook Chapter 8 application of integrals problems helps in improving accuracy and understanding different problem types. Revising with a Class 12 NCERT Maths Book Chapter 8 formula sheet can save time during exams.

Solving the Application of Integrals Class 12 NCERT Revised Book solutions will also help students tackle Class 12 Maths Chapter 8 important questions effectively. Downloading the NCERT detailed solutions for Class 12 Math Chapter 8 PDF free allows for on-the-go revisions. Focusing on both theoretical understanding and practical application ensures students excel in this chapter while building a strong foundation for advanced mathematical studies.

Important Points in Class 12 Maths Chapter 8 Application of integrals for Exams

Key topics include calculating areas under curves and between curves using definite integrals. Focus on solved examples, Class 12 Maths Chapter 8 exercise 8.1 and the formula sheet. Practice previous year questions, miscellaneous exercises and important applications to strengthen problem-solving and conceptual clarity for exams.

Class XII Mathematics Chapter 8 Exercise 8.1 in Hindi and English Medium with Miscellaneous Exercises to view online for new session. Class 12 NCERT exercises solution for other subjects like Physics, Chemistry, Biology, Physical Education, and Business studies are also available in PDF e-books to download. To prepared board exams, CBSE Board exam papers with answers and solutions are given here.

NCERT Solutions for class 12 Maths Chapter 8 all exercises including miscellaneous exercise are given below to download free in PDF updated for new academic session 2025-26. Download NCERT Books 2025-26 based on latest CBSE Syllabus for new academic session. Join the discussion forum to ask your doubts related to NIOS and CBSE Board.

1. Find the area of the region in the first quadrant enclosed by the y-axis, the line y = x and the circle x² + y² = 32, using integration. [Delhi 2015C]
2. Using integration find the area of the triangle formed by positive x-axis and tangent and normal to the circle x² + y² = 4 at (1, √3). [Delhi 2015]
3. Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32. [Delhi 2014]
4. Using integration, find the area bounded by the curve x² = 4y and the line x = 4y – 2. [Delhi 2013]
5. Using integration, find the area of the region enclosed between the two circles x² + y² = 4 and (x – 2)² + y² = 4. [Delhi 2013]

1. Using integration, find the area of region bounded by the triangle whose vertices are (-2, 1), (0, 4) and (2, 3). [Delhi 2017]
2. Find the area bounded by the circle x² + y² = 16 and the line √3 y = x in the first quadrant, using integration. [Delhi 2017]
3. Find the area of the region bounded by the y-axis, y = cos x and y = sin x, x lies in [0, π/2]. [CBSE Sample Paper 2017]

4. Using integration find the area of the region {(x, y): x² + y² ≤ 2ax, y² ≥ ax, x, y ≥ 0}. [Delhi 2016]
5. Using integration, find the area bounded by the tangent to the curve 4y = x² at the point (2, 1) and the lines whose equations are x = 2y and x = 3y – 3. [CBSE Sample Paper 2016]