CBSE Class 12th Mathematics Chapter 8 - Applications of the Integrals Important Questions with Answers

You should focus on solving CBSE Class 12th Mathematics Chapter 8: Applications of the Integrals important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 8 questions, you will be solving exam-oriented questions only.

Never Miss an Exam Update

The chapter Applications of the Integrals in CBSE Class 12 Mathematics plays a crucial role in understanding how integration is applied in real-world problems. The chapter develops basic integration principles to showcase their use in area calculations beneath curves as well as region area calculations and advanced volume determination. Effective mastery of this subject serves students before their board examinations because it prepares them for future calculus admissions and engineering and mathematical study pathways. Students can achieve effective preparation through this page which delivers complete essential questions and solutions about Applications of the Integrals. The set of questions explores every topic from Chapter 7 starting with finding areas between two curves while also addressing definite integrals and their corresponding geometric interpretations. Diverse questions in this material allow students to reinforce their understanding while developing efficient problem-solving abilities. Students who solve these vital questions find improvement in their analytical abilities and develop better knowledge of integral usage. Students will find various types of questions in this resource including short and long-answer problems along with CBSE-aligned test-oriented problems. The solutions provide students with each step needed to correctly solve application problems that require integration.

The important questions in this document will help students prepare for board examinations and competitive tests. Knowledge of Applications of the Integrals will lead to better examination results and prepare students to handle advanced mathematical problems with confidence. Prepare thoroughly with the most important questions of CBSE Class 12th Mathematics Chapter 8 - Applications of the Integrals. You can first cover the CBSE Class 12th Mathematics syllabus to understand the key topics and then start solving the CBSE Class 12th Mathematics Chapter 8 - Applications of the Integrals Important Question to get a better understanding of your preparation level. Start practicing now.

Are you feeling lost and unsure about what career path to take after completing 12th standard?

Say goodbye to confusion and hello to a bright future!

Was this article helpful?

0 Upvotes

0 Downvotes

Using integration, find the area of ? ABC, the coordinates of whose vertices are A (2, 5), B(4, 7) and C(6, 2). (Delhi 2019, 2011: All India 2010C)

Question 2.

Using integration, find the area of triangle whose vertices are (2, 3), (3, 5) and (4, 4). (Delhi 2019)

Question 3.

Find the area of the region lying above X-axis and included between the circle x² + y² = 8x and inside the parabola y² = 4x (Delhi 2019)

Question 4.

Using integration, prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts. (Delhi 2019, 2009; All India 2015)

Question 5.

Using method of integration, find the area of the triangle whose vertices are (1, 0), (2, 2) and (3, 1). (All India 2019)

Question 6.

Using integration, find the area of the region enclosed between the two circles
x² + y² = 4 and (x – 2)² + y² = 4. (All India 2019, 2010C: Delhi 2013, 2008)

Question 7.

Using integration, find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4. (All India 2019, 2011C; Delhi 2011)

Question 8.

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. (CBSE 2018; Delhi 2014)

Question 9.

Using integration, find the area of the region : {(x, y): 0 ? 2y ? x², 0 ? y ? x, 0 ? x ? 3}. (CBSE 2018 C)

Question 10.

Using integration, find the area of region bounded by the triangle whose vertices are (- 2, 1), (0, 4) and (2, 3). (Delhi 2017)

Question 1.

Find the area bounded by the circle x² + y² = 16 and the line ?3y = x in the first quadrant, using integration. (Delhi 2017)

Question 2.

Using the method of integration, find the area of the ?ABC, coordinates of whose vertices are A (4, 1), B(6, 6) and C (8, 4). (All India 2017)

Question 3.

Find the area enclosed between the parabola 4y = 3x² and the straight line 3x – 2y + 12 = 0. (All India 2017)

Question 4.

Using integration, find the area of the region
{(x, y): x² + y² ? 2ax, y² ? ax;x, y ? 0}. (Delhi 2016)

Question 5.

Using integration, find the area of the triangular region whose vertices are (2, – 2), (4, 3) and (1, 2). (All India 2016)

Question 6.

Using integration, find the area of the region bounded by the curves y = \(\sqrt{4-x^{2}}\), x² + y² – 4x = 0 and the x-axis. (Foreign 2016)

Question 7.

Using integration, 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. (Delhi 2015C)