NCERT Solutions of class 12 maths exercise 8.2 of chapter 8-Application of Integrals - Future Study Point

NCERT Solutions of class 12 maths exercise 8.2 of chapter 8-Application of Integrals

Class 12 ex 8.2 maths

NCERT Solutions of class 12 maths exercise 8.2-Application of Integrals 

NCERT Solutions of class 12 maths exercise 8.2 of chapter 8-Application of Integrals are the solutions of class 12 NCERT maths chapter 8 exercise 8.2- Applications of integrals that are created by future study point for the purpose of clearing the concept of the chapter-Application of integrals. All these NCERT solutions of exercise 8.1 are well explained by a step by step ways in order to be assessable for every student of class 12.

Applications of integrations are used in calculating the area, volume, mass, and density of the different types of shapes of the figure but exercise 8.2  is based on the area of curves covered by different kinds of curves.

Here in future study point, you can study science and maths NCERT solutions, sample paper, and solutions of previous year question papers. The technics of solving maths questions and achieving 100 % marks in maths , science special notes, preparation of competitive exams , science and maths e-book, and carrier in online jobs(latest jobs).

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

Class 12 ex 8.2 maths


You can also study NCERT solutions Class 12 Maths

Exercise 8.1-Application of Integrals

Exercise 8.3 – Application of Integrals

Miscellaneous exercise -Application of Integrals

Exercise 7.1- Integrals

Exercise 7.2-Integral

Exercise 7.3-Integrals

NCERT Solutions of class 12 maths exercise 8.2-Application of Integrals 

Q1. Find the area of circle 4x² + 4y² = 9 which is interior to the parabola x²= 4y.

Ans.We are given the equation of circle

4x² + 4y² = 9

Equation of parabola is given to us

x²= 4y……..(ii)

Equation of circle shows that its centre is at (0,0) radius is 3/2

Solving (i) and (ii) equations we get that parabola and circle intersect each other in first quadrant at (√2,1/2) and second quadrant at (-√2, 1/2)

class 12 ex 8.2 Q1


Area  interior to parabola=2×area of  OBC

Area of  OBC= area of OPBC -area of OPB

Area of OPBC

From (i) equation, we have


Area of OPB

Where y is equation of a parabola

x² = 4y


Hence the  area of OBC

Area  interior to parabola (OBCD)

NCERT Solutions of class 12 maths exercise 8.2-Application of Integrals 

Q2. Find the area bounded by the curves (x-1)² + y² = 1 and x² + y² =1.

Ans.We are given the equations of circle (x-1)² + y² = 1 and x² + y² =1,solving both of these equation for getting point of intersecting

class 12 ex 8.2 Q2


Both equations of the circle show that their centre lies at (1,0) and (0,0)

(x-1)² + y² = 1

x² +1 -2x +y² =1

x² = 2x – y², putting in equation x² + y² =1

2x – y² + y² = 1

2x = 1⇒ x=1/2,putting in x² + y² =1

y² = 1-1/4

y= ±√3/2

Hence the points of intersection of the both circle are (1/2, √3/2) and (1/2, -√3/2)

Solving both equation for the value of y

y = √[1-(x²-1)]….(i)  and y =√( 1 -x²)……(ii)

Required area = ar ABDO= ar ABDC + arAODC

ar AODC= 2×ar AOC ( Area of AODC is symmetric about x-axis)

ar AOC

As seen in the figure

Applying the integral formula


Therefore ar AODC

ar ABDC= 2×ar ABC ( Area of ABDC is symmetric about x-axis)

From the figure

ar ABC

Applying the integral formula



Required area = ar ABDO

You can compensate us by depositing a little money

Paytm number 9891436286

The money collected by us will be used for the education of poor students who leaves their study because of lack of money.

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution







Scroll to Top