NCERT Solutions - Exercise 8.2 : Application of Integrals

# Exercise 8.2 : Application of Integrals NCERT Solutions | Mathematics (Maths) for JEE Main & Advanced PDF Download

``` Page 1

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

Exercise 8.2                                                                Page No: 371

1. Find the area of the circle  which is interior to the parabola

Solution:
Step 1: Equation of the circle is
……….(1)

Here, centre of circle is (0, 0) and radius is 3/2
Equation of parabola is  …..(2)
Step 2: To find values of x and y
Put  in equation (1),

Page 2

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

Exercise 8.2                                                                Page No: 371

1. Find the area of the circle  which is interior to the parabola

Solution:
Step 1: Equation of the circle is
……….(1)

Here, centre of circle is (0, 0) and radius is 3/2
Equation of parabola is  …..(2)
Step 2: To find values of x and y
Put  in equation (1),

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

or
or
Find the value of x:
Put  in ,

Put  in ,

=>
Therefore, Points of intersections of circle (1) and parabola (2) are
A and B
Step 3: Area OBM = Area between parabola (2) and y-axis
=

=
Page 3

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

Exercise 8.2                                                                Page No: 371

1. Find the area of the circle  which is interior to the parabola

Solution:
Step 1: Equation of the circle is
……….(1)

Here, centre of circle is (0, 0) and radius is 3/2
Equation of parabola is  …..(2)
Step 2: To find values of x and y
Put  in equation (1),

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

or
or
Find the value of x:
Put  in ,

Put  in ,

=>
Therefore, Points of intersections of circle (1) and parabola (2) are
A and B
Step 3: Area OBM = Area between parabola (2) and y-axis
=

=

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

=  =
=  ……….(3)
Step 4: Now area BDM = Area between circle (1) and y-axis
=

=

=
=
Page 4

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

Exercise 8.2                                                                Page No: 371

1. Find the area of the circle  which is interior to the parabola

Solution:
Step 1: Equation of the circle is
……….(1)

Here, centre of circle is (0, 0) and radius is 3/2
Equation of parabola is  …..(2)
Step 2: To find values of x and y
Put  in equation (1),

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

or
or
Find the value of x:
Put  in ,

Put  in ,

=>
Therefore, Points of intersections of circle (1) and parabola (2) are
A and B
Step 3: Area OBM = Area between parabola (2) and y-axis
=

=

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

=  =
=  ……….(3)
Step 4: Now area BDM = Area between circle (1) and y-axis
=

=

=
=

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals
=
=
=  …….(4)
Step 5.
Required shaded area = Area AOBDA = 2 (Area OBD) = 2 (Area OBM + Area MBD)
=  =
=
=  =
=
2. Find the area bounded by the curves  and
Solution:
Equations of two circles are

……….(1)

Page 5

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

Exercise 8.2                                                                Page No: 371

1. Find the area of the circle  which is interior to the parabola

Solution:
Step 1: Equation of the circle is
……….(1)

Here, centre of circle is (0, 0) and radius is 3/2
Equation of parabola is  …..(2)
Step 2: To find values of x and y
Put  in equation (1),

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

or
or
Find the value of x:
Put  in ,

Put  in ,

=>
Therefore, Points of intersections of circle (1) and parabola (2) are
A and B
Step 3: Area OBM = Area between parabola (2) and y-axis
=

=

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

=  =
=  ……….(3)
Step 4: Now area BDM = Area between circle (1) and y-axis
=

=

=
=

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals
=
=
=  …….(4)
Step 5.
Required shaded area = Area AOBDA = 2 (Area OBD) = 2 (Area OBM + Area MBD)
=  =
=
=  =
=
2. Find the area bounded by the curves  and
Solution:
Equations of two circles are

……….(1)

NCERT Solutions for Class 12 Maths Chapter 8-Application of
integrals

And  ……….(2)
From equation (1),
Put this value in equation (2),

Put  in ,

The two points of intersections of circles (1) and (2) are  and .
```

## Mathematics (Maths) for JEE Main & Advanced

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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