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

The NCERT solutions of miscellaneous exercise of chapter 8-Application of Integrals are a summary of all the methods used in all the exercises of chapter 8-Application of Integrals, therefore in this respect, NCERT solutions of miscellaneous exercise are very important for students.All the questions of miscellaneous exercise are solved by the expert by a step-by-step method so each student will understand the solution clearly.

Click for online shopping

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

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

Exercise 8.1-Application of Integration

Exercise 8.2-Application of Integration

Exercise 8.3-Application of Integration

NCERT Solutions of Maths for Class 12 Miscellaneous exercise -Application of Integrals

Click for online shopping

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

Q1. Find the area under the given curve and given lines

(i) y = x² , x = 1, x =2 and x-axis

(ii) y = x⁴, x=1, x= 5 and x-axis

Ans.

(i) We are given the curve y = x²  and the lines  x = 1, x =2

 

 

 

 

 

 

 

 

 

Area covered by the curve,x-axis and the given lines = arABCD

(ii) We are given the curve y = x⁴, x=1, x= 5 and the lines  x = 1, x =2

 

 

 

 

 

 

 

 

Area covered by the curve, x-axis and the given lines = arABCD

Q2. Find the area between the curves y = x and y = x²

Ans. We are given the equations of curve y = x² and y = x

Putting y = x, in y = x²

x = x² ⇒ x= 0 and x =1,again putting x = 0 and x= 1 in one of the equations, we get y=0 and y=1

Therefore both of curve and the line intersect each other at origin (0,0) and (1,1)

 

 

 

 

 

 

 

 

Area covered by the line and the curve , area OCB = ar ΔOAB – ar OABCO

ar OABCO = 1/3 sq.unit

OA = 1 unit and AB = 1 unit

Q3. Find the area of the region lying in the first quadrant and bounded by y = 4x², x = 0, y =1 and y = 4.

Ans. The given curve is y = 4x² and the lines are x = 0, y =1 and y = 4.

 

 

 

 

 

 

 

 

The area covered by the curve y = 4x² and the lines are x = 0(y-axis), y =1, and y = 4 is ar ABCD

From the equation of curve, y = 4x², we have   

 

Q4. Sketch the graph of      and evaluate   

rom the equation of curve, y = 4x², we have   

 

Latest Laptops and Desktops on very small EMI:no extra cost

Q4. Sketch the graph of      and evaluate   

Ans.Solutions of the given equation 

x	-6	-5	-4	-3	-2	-1	0
y	3	2	1	0	1	2	3

The graph of the given equation is drawn as follows

 

 

 

 

 

 

 

 

 

=  – 9 + 18 = 9

Q5. Find the area bounded by the curve y = sinx between x = 0 and x = 2π.

Ans.The graph of the curve y = sinx between x = 0 and x = 2π, is shown below

 

 

 

 

 

 

 

The area bounded by the curve y = sinx, x = 0 and x = 2π

=Area of OAB + area of BCD

= 2 + 2 = 4 sq.unit

You can study

Click the link here for rest of the solutions or study the following

 Class 11 Chemistry

Chapter 1-Some basic concepts of chemistry

 Class 11 Physics

Chapter 1- Physical World

Paytm number 9891436286

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

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 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

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 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

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