Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals, which includes thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Solutions for Class 12 provide useful solutions for improving conceptual knowledge.
The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12pupils perform well in upcoming competitive exams.
The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals
The concepts covered in Class 12 Maths covered in Chapter 8 Application Of Integrals of NCERT Solutions are as follows:
8.1 Introduction
This part provides a review of the concepts of determining areas circumscribed by a curve, defining a definite integral as the limit of a sum, and introducing the use of integrals in applications such as the area under simple curves, between lines, parabolas, and ellipses.
Integration can be used to calculate a function’s average value.
The amount of rain that fell on a given day followed an R curve with specific boundaries. We get the average amount of rainfall for that day by integrating the provided function from limit x to limit y.
8.2 Area under simple curves
Using the formula, this section defines the region bounded by the curve y = f(x). For your convenience, a few samples are provided.
Assume you and your sibling are sharing a circular blanket. If the two of you are willing to compromise, the extent to which you will not be covered will be determined by the blanket’s size. We describe it mathematically as the area under the blanket that is available to the two of you.
These types of issues are classified as analyses of the area under curves.
8.2.1 The surface area of a region is defined by a curve and a line.
The area of a space can be calculated using a line and a circle, a line and a parabola, or a line and an ellipse. A few images help to explain the calculation procedure.
8.3 Area between Two Curves
This section contains solved questions that demonstrate how to find the area between two curves. According to the article, the area may be calculated by dividing the region into a number of little parts and then summing the area of those tiny pieces. If the little fragments are vertical in shape, it is easy to locate the location.
NCERT Solutions for Class 12 Maths Chapter 8 can be used as a quick reference to help students understand complicated concepts.
Students will work with numerous Integrals applications in this chapter of NCERT Solutions for Class 12 Maths. The following are some of the most important concepts:
- The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) is given by the formula:
Area = ∫baydx =∫baf(x)dx∫abydx=∫abf(x)dx
- The area of the region enclosed between two curves y = f (x), y = g (x) and the lines x = a, x = b is given by the formula,
Area = ∫ba∫ab; where f(x) ≥ g(x) in [a, b]
- If f (x) ≥ g (x) in [a, c] and f (x) ≤ g (x) in [c, b], a < c < b, then
Area = ∫ca+∫bc∫ac+∫cb
NCERT Solutions For Class 12 Maths Chapter 8 Exercises:
The number of questions given under below exercises:
Exercise 8.1 Solutions : 13 Questions (8 Long, 3 Short, 2 MCQs)
Exercise 8.2 Solutions : 7 Questions(5 Long, 2 MCQs)
Miscellaneous Exercise Solutions: 19 Questions (8 Long, 7 Short, 4 MCQs)
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals
The topics covered in NCERT Solutions for Class 12 Maths Chapter 8-Application of Integrals are as follows:
| Exercise | Topic |
| 8.1 | Introduction |
| 8.2 | Area under Simple Curves |
| 8.3 | Area between Two Curves. |
| Others | Miscellaneous Q&A |
Key Features of NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals
- Subject specialists assisted in the preparation of these NCERT Solutions.
- Assist students in reinforcing their fundamental understanding of integral applications.
- Content that is well-structured.
- Diagrams are used to answer all of the questions.
- Assist kids with their homework and competitive tests.
Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 8
- How can we score full marks in NCERT Solutions for Class 12 Maths Chapter 8?
- Are NCERT Solutions for Class 12 Maths Chapter 8 PDF enough to score well in the term – II exams?
- Why should I study Chapter 8 of NCERT Solutions for Class 12 Maths?
1. How can we score full marks in NCERT Solutions for Class 12 Maths Chapter 8?
Experts at Infinity Learn created the NCERT Solutions for Class 12 Maths Chapter 8 after completing an extensive study on each concept. Every minor aspect is thoroughly discussed in order to assist students to perform well on the class test as well as the second-term exams. It also assists pupils in completing their assignments on time and without difficulties.
2. Are NCERT Solutions for Class 12 Maths Chapter 8 PDF enough to score well in the term – II exams?
NCERT Solutions for Class 12 Maths Chapter 8 are accessible in PDF format, and students can download and use them at their leisure. The solutions are developed by Infinity Learn’s highly experienced faculty using the most recent CBSE Syllabus and norms. The exercise-by-exercise solutions assist students in gaining a general understanding of the subjects that are crucial for second-term exams. Students’ time management and problem-solving abilities will improve if they practice these questions on a regular basis.
3. Why should I study Chapter 8 of NCERT Solutions for Class 12 Maths?
The NCERT Solutions for Class 12 Maths Chapter 8 are curated by a team of Infinity Learn experts with extensive knowledge in the subject. Students are encouraged to use the solutions PDF while working on the textbook problems to reinforce their understanding of integral applications. The questions are answered with a graphical depiction to help pupils understand the ideas. Apart from the second-term test preparation, students will be well-prepared to take a variety of competitive exams.
