NCERT Solutions for class 12 Maths Chapter 8 Application of integrals Exercise 8.1 and Exercise 8.2 in Hindi and English Medium with Miscellaneous Exercises to view online or in PDF file format to free download for new session 2022-2023. Class 12 NCERT solutions for other subjects (Physics, Chemistry, Biology, Physical Education, Business studies, etc.) are also available in PDF e-books to download. download CBSE Board exam papers with answers and solutions. Join the Discussion Forum to share your knowledge.

## NCERT Solutions for class 12 Maths Chapter 8

• ### Class 12 Maths Chapter 8 Solutions in English Medium

 Class: 12 Subject: Maths Chapter 8: Application of integrals

### 12th Maths Chapter 8 Solutions

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 2022-23. Download NCERT Books 2022-23 based on latest CBSE Syllabus for new academic session. Join the discussion forum to ask your doubts related to NIOS and CBSE Board.

• ### Class 12 Maths Chapter 8 Solutions in Hindi Medium

#### Class 12 Maths Exercise 8.1 Solutions in Videos

Class 12 Maths Chapter 8 Exercise 8.1 Solution
Class 12 Maths Exercise 8.1 Solution in Hindi

#### Class 12 Maths Exercise 8.2 Solutions in Videos

Class 12 Maths Chapter 8 Exercise 8.2 Solution
Class 12 Maths Exercise 8.2 Solution in Hindi

#### Class 12 Maths Chapter 8 Miscellaneous Exercise in Videos

Class 12 Maths Chapter 8 Miscellaneous Solution
Class 12 Maths Chapter 8 Miscellaneous in Hindi
• ### Class 12 Maths Chapter 8 Solutions in PDF

#### Important Questions for practice

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]

##### Questions from Board Papers

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]

### What are the topics covered by ‘Applications of Integration’?

In Class 12 Chapter 8 ‘Applications of Integration’ deals with a specific application of integrals to find the area under simple curves, area between lines and arcs of circles, parabolas and ellipses, and finding the area bounded by the above said curves.

### Fill in the blank: The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is _______.

37/3 square units.

### Fill in the blank: The area of the region bounded by the curve y = x2 + x, x-axis and the line x = 2 and x = 5 is equal to ________.

297/6 square units.                                              