Download CBSE Class 12 Mathematics Application Of Integration Notes in PDF format. All Revision notes for Class 12 Mathematics have been designed as per the latest syllabus and updated chapters given in your textbook for Mathematics in Class 12. Our teachers have designed these concept notes for the benefit of Class 12 students. You should use these chapter wise notes for revision on daily basis. These study notes can also be used for learning each chapter and its important and difficult topics or revision just before your exams to help you get better scores in upcoming examinations, You can also use Printable notes for Class 12 Mathematics for faster revision of difficult topics and get higher rank. After reading these notes also refer to MCQ questions for Class 12 Mathematics given on studiestoday
Revision Notes for Class 12 Mathematics Chapter 8 Applications of Integrals
Class 12 Mathematics students should refer to the following concepts and notes for Chapter 8 Applications of Integrals in Class 12. These exam notes for Class 12 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks
Chapter 8 Applications of Integrals Notes Class 12 Mathematics
(A) KEY CONCEPTS
1. AREA LYING BELOW THE X-AXIS:
If f(x)≤0 for a≤x≤b,then the graph of y=f(x) lies below x-axis Therefore area bounded by the curve y=f(x),x-axis and the ordinates x=a and x=b is given by
2. AREA LYING ABOVE THE X-AXIS:
The area enclosed by the curve y= f(x), x-axis & between the ordinate at x=a & x=b is given
3. AREA LYING ON RIGHT OF Y-AXIS :
Area bounded by the curve x=f(y),y-axis and the abscissa y=c and y=d is given by
4. AREA LYING ON LEFT OF Y-AXIS:
The area enclosed by the curve x= f(y), y-axis & between the abscissa at y=c & y=d is given by :
5. AREA BOUNDED BY TWO CURVES
Area bounded by the two curves y = f(x) & y = g(x) where f1(x) f2(x) in a , b & between the ordinate x=a & x=b is given by
IMPORTANT FORMULAE TO USE :
Important Notes
1. If the equation of the curve contains only even powers of x, then the curve is symmetrical about y-axis
2. If the equation of the curve contains only even powers of y, then the curve is symmetrical about x-axis.
3. If the equation of the curve remains unchanged when x is replaced by –x and y by –y, then the curve is symmetrical in opposite quadrants.
4. If the equation of the curve remains unchanged when x and y are interchanged ,then the curve is symmetrical about the line y=x
1. Find the area of the region {(x,y):x2 ≤ y ≤ x }
Sol. The required area is bounded between two curves y =x2 and y= x . Both of these curves are symmetric about y-axis and shaded region in the fig. shows the region whose area is required.
Therefore, required area =2× area of region R1
Now to find point of intersection of curves y =x2 and y= x , we solve them simultaneously.
Clearly, region R1 is in first quadrant, where x>0
x =x => y =x…………….(i)
y =x2…………….(ii)
either x = 0 or x = 1
The limits are , when x=0, y=0 and when x=1, y=1
So points of intersection of the curve are o(0,0) and A(1,1)
Now, required area = 2× area of region R1
Please click the link below to download CBSE Class 12 Mathematics Application of Integration.
| CBSE Class 12 Mathematics Relations And Functions Notes Set A |
| CBSE Class 12 Mathematics Relations And Functions Notes Set B |
| CBSE Class 12 Mathematics Matrices And Determinants Notes |
| CBSE Class 12 Mathematics Continuity And Differentiability Notes |
| CBSE Class 12 Mathematics Application Of Derivative Notes |
| CBSE Class 12 Mathematics Integration Notes |
| CBSE Class 12 Mathematics Application Of Integration Notes |
| CBSE Class 12 Mathematics Differential Equation Notes |
| CBSE Class 12 Mathematics Vectors And 3D Notes |
| CBSE Class 12 Mathematics Linear Programming Notes |
| CBSE Class 12 Mathematics Probability Notes |
| CBSE Class 12 Mathematics Important Concepts For All Chapters |
CBSE Class 12 Mathematics Chapter 8 Applications of Integrals Notes
We hope you liked the above notes for topic Chapter 8 Applications of Integrals which has been designed as per the latest syllabus for Class 12 Mathematics released by CBSE. Students of Class 12 should download and practice the above notes for Class 12 Mathematics regularly. All revision notes have been designed for Mathematics by referring to the most important topics which the students should learn to get better marks in examinations. Studiestoday is the best website for Class 12 students to download all latest study material.
Notes for Mathematics CBSE Class 12 Chapter 8 Applications of Integrals
Our team of expert teachers have referred to the NCERT book for Class 12 Mathematics to design the Mathematics Class 12 notes. If you read the concepts and revision notes for one chapter daily, students will get higher marks in Class 12 exams this year. Daily revision of Mathematics course notes and related study material will help you to have a better understanding of all concepts and also clear all your doubts. You can download all Revision notes for Class 12 Mathematics also from www.studiestoday.com absolutely free of cost in Pdf format. After reading the notes which have been developed as per the latest books also refer to the NCERT solutions for Class 12 Mathematics provided by our teachers
Chapter 8 Applications of Integrals Notes for Mathematics CBSE Class 12
All revision class notes given above for Class 12 Mathematics have been developed as per the latest curriculum and books issued for the current academic year. The students of Class 12 can rest assured that the best teachers have designed the notes of Mathematics so that you are able to revise the entire syllabus if you download and read them carefully. We have also provided a lot of MCQ questions for Class 12 Mathematics in the notes so that you can learn the concepts and also solve questions relating to the topics. All study material for Class 12 Mathematics students have been given on studiestoday.
Chapter 8 Applications of Integrals CBSE Class 12 Mathematics Notes
Regular notes reading helps to build a more comprehensive understanding of Chapter 8 Applications of Integrals concepts. notes play a crucial role in understanding Chapter 8 Applications of Integrals in CBSE Class 12. Students can download all the notes, worksheets, assignments, and practice papers of the same chapter in Class 12 Mathematics in Pdf format. You can print them or read them online on your computer or mobile.
Notes for CBSE Mathematics Class 12 Chapter 8 Applications of Integrals
CBSE Class 12 Mathematics latest books have been used for writing the above notes. If you have exams then you should revise all concepts relating to Chapter 8 Applications of Integrals by taking out a print and keeping them with you. We have also provided a lot of Worksheets for Class 12 Mathematics which you can use to further make yourself stronger in Mathematics
You can download notes for Class 12 Mathematics Chapter 8 Applications of Integrals for latest academic session from StudiesToday.com
Yes, you can click on the link above and download notes PDFs for Class 12 Mathematics Chapter 8 Applications of Integrals which you can use for daily revision
Yes, the notes issued for Class 12 Mathematics Chapter 8 Applications of Integrals have been made available here for latest CBSE session
You can easily access the link above and download the Class 12 Notes for Mathematics Chapter 8 Applications of Integrals for each topic in Pdf
There is no charge for the notes for CBSE Class 12 Mathematics Chapter 8 Applications of Integrals, you can download everything free of charge
www.studiestoday.com is the best website from which you can download latest notes for Chapter 8 Applications of Integrals Mathematics Class 12
Come to StudiesToday.com to get best quality topic wise notes for Class 12 Mathematics Chapter 8 Applications of Integrals
We have provided all notes for each topic of Class 12 Mathematics Chapter 8 Applications of Integrals as per latest CBSE syllabus