Daily Practice Problems

Class 12 Maths

Application of Integrals

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 4x^{2} + 4y^{2} = 9 which is interior to the parabola x^{2} = 4y.

**Question 3:**

Find the area bounded by curves (x – 1)^{2} + y^{2} = 1 and x^{2} + y^{2} = 1.

**Question 4:**

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

**Question 5:**

Find the smaller area enclosed by the circle x^{2} + y^{2} = 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 x^{2} = 4y and the line x = 4y – 2.

**Question 8:**

Find the area bounded by the curves y^{2} = 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 – x^{2}) 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 = x^{3} 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 = x^{3}, 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 y^{2} = 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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**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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