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Daily Practice Problems
Class 12 Maths
Application of Integrals

Question 1:

Using integration finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).

Question 2:

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.

Question 3:

Find the area bounded by curves (x – 1)2 + y2 = 1 and x2 + y2 = 1.

Question 4:

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12.

Question 5:

Find the smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2.

Question 6:

Find the area bounded by the curve y = x|x|, x-axis and the ordinates x = –1 and x = 1.

Question 7:

Find the area bounded by the curve x2 = 4y and the line x = 4y – 2.

Question 8:

Find the area bounded by the curves y2 = 4x and y = x.

Question 9:

Area bounded by the curve y = sin x and the x-axis between x = 0 and x = 2π is ______.

Question 10:

Area of the region bounded by the curve y = √(49 – x2) and the x-axis is _____.

Question 11:

Area of the region bounded by the curve x = 2y + 3, the y-axis and between y = -1 and y = 1 is _____.

Question 12:

The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is _____.

Question 13:

Find the area of the region bounded by the curve y² = x, the y-axis and between y = 2 and y = 4.

Question 14:

The area bounded by the curve y = x3, the x-axis and two ordinates x = 1 and x = 2 is _____.

Question 15:

Find the area of the region bounded by the curve y = 1/x, x-axis and between x = 1, x = 4.

Question 16:

The area of the region bounded by the curve y² = x, the y-axis and between y = 2 and y = 4 is 56/3 sq units. State whether it is true or false?

Question 17:

Find the area of the region bounded by the circle x² + y² = 1.

Question 18:

What is the area of the parabola y2 = x bounded by its latus rectum?

Question 19:

Find the area of the region bounded by the curve y = e-2x and x-axis for x (-1, 1).

Question 20:

Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

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## Problem-solving on Class 12 Maths Application of Integrals NCERT Chapter 8 after learning a theoretical concept is crucial for several reasons:

1. Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 12 Maths Application of Integrals you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
2. Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 12 Maths Application of Integrals NCERT Chapter 8, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
3. Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
4. Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Application of Integrals Class 12 Maths in practical scenarios helps you remember them better than passive reading or memorization.
5. Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Application of Integrals Class 12 Maths Notes on LearnoHub.com
6. Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Application of Integrals. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
7. Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Application of Integrals Class 12 Maths Online Tests at LearnoHub.com.
8. Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
9. Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
10. Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Application of Integrals Class 12 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on Class 12 Maths Application of Integrals NCERT Chapter 8

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 12 Maths Application of Integrals NCERT Chapter 8 useful.

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• Application of Integrals Class 12 Maths Best videos
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