NCERT Solutions for Class 12 Maths Chapter 8
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NCERT Solutions for Class 12 Maths Chapter 7 is all about Integrals. Application of Integrals Class 12 NCERT Solutions is one of the most challenging chapters that students have to study in their Mathematics syllabus.
Class 12 Maths Chapter 8 Exercise 8.1
This exercise has a total of 13 questions that are provided with NCERT Solutions for Class 12 Maths Chapter 8.
Question 1 and Question 2 – These questions require students to find the area of a region bounded by a curve, two parallel lines and the x-axis in the first quadrant.
Question 3 - It is similar to the previous questions. The only difference is that the area has to be plotted on the y-axis instead of the x-axis. Our Integrals Class 12 NCERT Solutions come with step by step explanations that make it easy to understand how to solve such problems.
Question 4 and Question 5 – Both these questions in the Application of Integrals Class 12 NCERT Solutions deal with the calculation of the area of a region bound by an ellipse.
Question 6 - Students need to find out the area of a region in the first quadrant enclosed by the x-axis, a line, and a circle. The central concept of forming the equation of a line in the format of y = mx+c and using the circle equation is what is needed to be done.
Question 7 – It requires students to find the area of a smaller part of a circle cut off by a line.
Question 8 – It is a question wherein the area between a parabola and a line is divided into two equal parts by a line x = a. The students are asked to find the value of ‘a’.
Question 9 - Students need to calculate the area of the region bounded by a parabola and a line y=|x|. To answer this question, one must have knowledge about what parabola is and how to frame its equation.
Question 10 and Question 11 – These couple of questions in the Application of Integrals Class 12 NCERT Solutions require students to find out the area bounded by a curve and a line.
Question 12 – It is a multiple-choice question asking the students to figure out what will be the area lying in the first quadrant and bounded by a circle and the lines x=0 and x=2 be.
Question 13 – This question is much like the previous one. The only difference being, instead of a circle, this question has a curve, and the lines are y=3 and the y-axis.
Application of Integrals Class 12 NCERT Solutions is an essential topic since it plays a vital role in all the competitive exams and board examinations as well.
Class 12 Maths Chapter 8 Exercise 8.2
This exercise has 7 questions which are explained in detail in our NCERT Solution with shortcut techniques.
Question 1 - Students need to answer this question based on the calculation of the area of a circle which is interior to a parabola. Key concepts that students to focus on are -
How to formulate equations of curved surfaces?
How to calculate the area enclosed within curved surfaces?
In Question 2 – The answer to this question requires students to find out the area that is bounded by two curves.
Question 3 – Students need to calculate the area of the region bound by a curve, y-axis, and two lines y=x and x=3. Considering that such questions are a frequent occurrence in exam papers, our solutions bring you with the best step by step explanation that brings clarity to the idea behind the sum.
Questions 4 and 5 – It requires students to use the integration method to find out the area of the region bounded by a triangle whose vertices (Question 4) or equations of the side (Question 5) are mentioned.
Question 6 – This is a multiple-choice question wherein students are asked to find the smaller area enclosed by a circle and a line.
Question 7 – The last question of this exercise involves a multiple choice and requires students to calculate the area lying between a curve and a line.
Our Integrals Class 12 NCERT Solutions PDF make answering such questions a convenient affair for you and is coupled with shortcut techniques.
Apart from these two exercises, there is also a miscellaneous exercise in this chapter which helps you have a recapitulation of the entire topic. Our Application of Integrals Class 12 NCERT Solutions comprises answers to all such questions.
Class 12 Maths Chapter 8 Miscellaneous Exercise
The miscellaneous exercise of this chapter contains about 19 questions from topics all over the chapter. We provide NCERT Solutions Class 12 Maths Chapter 8 Miscellaneous Exercise that takes into account the concept of this complete chapter. Students can go through our solved examples of our NCERT books PDF to have a better idea about the Application of Integrals Class 12 NCERT Solutions.
To get a better grasp of the chapter the Application of Integrals Class 12 students need to understand a few fundamental theories like
Equation of a line,
Integrals of trigonometric entities.
If any student wants to pursue this subject as a prospect, this one chapter is crucial. To help you reduce your pain and effort, we bring you NCERT books PDF.
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