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.

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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)

 

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

Therefore

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

 

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

 

ar ABDC

Required area = ar ABDO

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

NCERT Solutions for class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

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NCERT Solutions for Class 10 Science

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

NCERT Solutions for class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

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NCERT solutions for class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

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