NCERT Solutions for class 12 Maths Chapter 8 Application of integrals in Hindi and English Medium for CBSE 2022-2023 exams.

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

### NCERT Solutions for class 12 Maths Chapter 8

Class XII Mathematics Chapter 8 Exercise 8.1 and Exercise 8.2 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.

### Class 12 Maths Chapter 8 all Exercises Solution

 Class: 12 Mathematics Chapter 8: Application of integrals Content: Exercises and Extra Questions Content Type: PDF, Text and Videos Format Medium: Hindi and English Medium

#### 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 Study Material

##### Important Questions for practice on Chapter 8 Class 12th Maths

1. Find the area of the region in the first quadrant enclosed by the y-axis, the line y = x and the circle xÂ² + yÂ² = 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 xÂ² + yÂ² = 4 at (1, âˆš3). [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 xÂ² + yÂ² = 32. [Delhi 2014]
4. Using integration, find the area bounded by the curve xÂ² = 4y and the line x = 4y â€“ 2. [Delhi 2013]
5. Using integration, find the area of the region enclosed between the two circles xÂ² + yÂ² = 4 and (x â€“ 2)Â² + yÂ² = 4. [Delhi 2013]

### What are the topics covered by â€˜Applications of Integrationâ€™?

In Class 12 Chapter 8 â€˜Applications of Integrationâ€™ 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.

##### 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 xÂ² + yÂ² = 16 and the line âˆš3 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, Ï€/2]. [CBSE Sample Paper 2017]

4. Using integration find the area of the region {(x, y): xÂ² + yÂ² â‰¤ 2ax, yÂ² â‰¥ ax, x, y â‰¥ 0}. [Delhi 2016]
5. Using integration, find the area bounded by the tangent to the curve 4y = xÂ² at the point (2, 1) and the lines whose equations are x = 2y and x = 3y â€“ 3. [CBSE Sample Paper 2016]