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Edited By Lovekush kumar saini | Updated on Jan 24, 2022 03:19 PM IST

RD Sharma books are the benchmark of CBSE Maths in India. These books are renowned for their detailed and concept-rich chapters. They cover all aspects of the chapter and are the best medium of preparation for CBSE students. Once students prepare from this book, they can rest assured that they have covered all concepts in detail.

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RD Sharma Class 12th Exercise 20.1 of Indefinite Integrals contains 30 questions, 22 of which are Level 1 and eight are Level 2. The Level 1 sums are relatively easier and can be completed swiftly. Level 2 sums, however, require some conceptual understanding and are slightly longer. RD Sharma solutions These questions are based on the area of the region bounded between line and parabola, curve and line, and many more by using integration and also draw a rough sketch of the graph of the function then evaluate the region. Students are suggested to complete this exercise efficiently with the help of the material provided by Career360.

Areas of Bounded Region exercise 20.1 question 2

Hereis equation of line

We can write

_{}

We get_{}

Consider as line intersecting the at point _{}

So required area_{}

_{}

Substituting the value of_{},

_{} _{}

Substituting the value of_{} ,

Areas of Bounded Region exercise 20.1 question 3

Find the shaded area

Find area of region bounded by parabola and the line

We have

… (i)

… (ii)

Required area shaded region

Areas of Bounded Region exercise 20.1 question 4

Solve area of integration.

Find area lying above the and under parabola

Areas of Bounded Region exercise 20.1 question 5

Draw rough sketch to indicate the region bounded between curve and line .Also find the area of region.

Represent parabola with vertex at line parallel to.

Since is symmetrical axis

Area of corresponding rectangle

Areas of Bounded Region exercise 20.1 question 6

Make rough sketch of graph of function , and determine the area enclosed by curve and ,line and .

, represent half parabola with vertex

represent a line parallel to and cutting axis at

Area required

Areas of Bounded Region exercise 20.1 question 7

Where

Sketch the graph of

Areas of Bounded Region exercise 20.1 question 8

Find area under curve above form to . Draw sketch of curve also.

represent a parabola with vertex and symmetric about where is

The rectangle move from to

Consider,

Areas of Bounded Region exercise 20.1 question 9

Draw the rough sketch of .Find area enclosed by curve and line

Areas of Bounded Region exercise 20.1 question 10

Draw rough sketch of graph of curveand evaluate area of region under curve and above

Since given equation

All power of and are even

A = Area of enclosed curve along

Areas of Bounded Region exercise 20.1 question 11

Sketch the region and find the area of region enclosed by using integration.

We have,

.........(i)

...........(ii)

From (i), we get

Since all power of and are equal

Areas of Bounded Region exercise 20.1 question 12

Draw a rough sketch of graph of function and evaluate the area enclosed between the curve and

We have

Since given equation

Areas of Bounded Region exercise 20.1 question 13

Required area area of shaded region

Areas of Bounded Region exercise 20.1 question 15

Use definite integral

Using definite integral, find area of circle

Centre

Radius

Hence,

Area of circle area of region

We know that

Since lies in first quadrant, value of is positive

Now,

Area of circle

Areas of Bounded Region exercise 20.1 question 16

Using integration, find area of region bounded by following curve making a rough sketch

We have

Intersect at and at

is

Let required area be since limits on are given we use horizontal strip to find area

Areas of Bounded Region exercise 20.1 question 17

Break the limit and find the value of integral.

Sketch the graph

Evaluate. What the value of integral represents on graph

Areas of Bounded Region exercise 20.1 question 18

Break the limit and find integral

Let's draw graph,

Required area

Areas of Bounded Region exercise 20.1 question 19

Find integral

Evaluate what does the value of integral represented on graph

We have,

intersect and at and

Now,

Integral represents the area enclosed between and

Areas of Bounded Region exercise 20.1 question 20

Use the concept of definite integrals.

Find area of region bounded by curve

Given curve,

Area of bounded curve and line

Areas of Bounded Region exercise 20.1 question 21

use definite integral.

Draw rough sketch of curve Find area between the curve and ordinate

_{}at_{}

Area of shaded region

Areas of Bounded Region exercise 20.1 question 22

You know about integral of

Draw rough curve . Find area between with ordinate

Areas of Bounded Region exercise 20.1 question 23

Curve,

Find area by curve and ordinate and

Areas of Bounded Region exercise 20.1 question 24

Use two graph of .

Show that area under curve between and are in ratio

............(ii)

From (i) and (ii)

Thus area of curve for and are in ratio

Areas of Bounded Region exercise 20.1 question 25

Each equal to

Use

Compare area under curve between

Apply reduction formula,

Apply reduction formula,

Areas of Bounded Region exercise 20.1 question 26

Use ellipse formula

Find area bounded by ellipse and ordinate and where and

Required area Area of region

Area of

We know that,

Since _{}in first quadrant, value of_{} is positive

Required area

Areas of Bounded Region exercise 20.1 question 27

Use definite integrals.

Find area of circle cut by the line

By solving equation and

Hence form diagram, we get

Required area

Areas of Bounded Region exercise 20.1 question 28

Use definite integral.

Find area of curve between ordinate and

Given

Required area

Areas of Bounded Region exercise 20.1 question 29

Use

Find area enclosed by curve

The given curve represents the parametric equation of ellipse.

Eliminating the parameter , we get,

This represent the Cartesian equation of the ellipse with centre . The co ordinates of the vertices are and .

Required area Area of the shaded region

Area of region

Areas of Bounded Region exercise 20.1 question 30

Use integration.

If area between curve and divide two equal part of line .find using integration.

Given curve

_{}

Let represent line

represent line

Since line divide the region in two equal parts

Area of Area of

.............(i)

Now,

From (i)

Take root on both sides

RD Sharma Class 12th Exercise 20.1 material is expert-created and complies with the CBSE syllabus. This means that students can refer to the solutions to finish their homework as well as prepare for exams. Additionally, as this material is updated to the latest version, students can ensure that all of the questions and their solutions are from the newest version of the book.

RD Sharma books have a history of being comprehensive and detailed. Unfortunately, this means that it contains a large number of unsolved exercise questions. To help students deal with this situation, Career360 has provided RD Sharma Class 12th Exercise 20.1 solutions to ensure that no question is left behind.

Moreover, teachers can't cover the entire syllabus through lectures due to online classes, so they give most of the questions as homework. We at Career360 understand this issue and provide solutions to help students cover the whole syllabus without inconvenience.

RD Sharma Class 12th Exercise 20.1 solutions are meant to guide students with detailed answers. In addition, it is readily available on Career360's website, which makes it even more helpful as students can access it right from their homes using a device with a browser and internet connection.

This material provides different ways to solve a question. Students can refer to it and choose the method that suits them best. Maths is a subject in which every step counts; even one slight mistake in a step can lead to the wrong answer. This is why students are required to practice the sums well and look for all types of problems. This material will help students get plenty of questions for better understanding.

As the solutions are conveniently available to students, it gives them even more confidence to solve questions as they have the option to check their progress with this material. Thousands of students have already started preparing RD Sharma Class 12th Exercise 20.1 material as it is convenient and easy to use. Students should start preparing if they don't yet know about this.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

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Download E-book1. Which is better for maths, RD Sharma or NCERT?

RD Sharma books are more detailed and contain exam-oriented questions. NCERT books are useful for basic education, but they don't get to the level of RD Sharma in the case of content.

2. Can I solve NCERT questions after preparing this material?

As RD Sharma books have a slight edge over NCERT materials, students can definitely solve NCERT questions after preparing from RD Sharma Class 12 Chapter 20 Exercise 20.1 material.

3. What is a bounded region?

Any curve or figure on a graph that is bounded on all sides is called a bounded region. It can also be an outcome of the intersection of two curves. For more information, check Class 12 RD Sharma Chapter 20 Exercise 20.1 Solutions.

4. How to calculate the area of a bounded region?

The area of a bounded region can be calculated using the integral of its function after applying the horizontal or vertical limits of the region. To know more, refer to RD Sharma Class 12 Solutions Areas of Bounded Region Ex 20.1.

5. Do the questions from this material appear in exams?

As RD Sharma books are widely used in CBSE schools, questions from RD Sharma Class 12 Solutions Chapter 20 Ex 20.1 could appear in exams.

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