# NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8 - Application of Integrals

NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 is similar to the exercise 8.1. Also it has linkages with the previous chapter. Exercise 8.2 Class 12 Maths consists of questions related to areas bounded by two different curves. NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 can be solved easily if the concept is understood from initial few questions. All other questions have the same concept used. Similar questions which are in this exercise are asked in Physics also, hence this exercise becomes more important. Students can find solutions to other exercises apart from this exercise from below mentioned NCERT exercise list.

Application of Integrals Exercise 8.1

Application of Integrals Miscellaneous Exercise

## **Application of Integrals**** Class 12 Chapter 8 Exercise****: 8.2**** **

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

** Answer: **

The area bounded by the circle and the parabola .

By solving the equation we get the intersecting point and

So, the required area (OBCDO)=2 times the area of (OBCO)

Draw a normal on the x-axis (M = )

Thus the area of OBCO = Area of OMBCO - Area of OMBO

S0, total area =

** Question:2 ** Find the area bounded by curves and .

** Answer: **

Given curves are and

Point of intersection of these two curves are

and

We can clearly see that the required area is symmetrical about the x-axis

Therefore,

Area of OBCAO = 2 Area of OCAO

Now, join AB such that it intersects the x-axis at M and AM is perpendicular to OC

Coordinates of M =

Now,

Area OCAO = Area OMAO + Area CMAC

Now,

Area of OBCAO = 2 Area of OCAO

Therefore, the answer is

** Question: 3 ** Find the area of the region bounded by the curves and .

** Answer: **

The area of the region bounded by the curves,

and is represented by the shaded area OCBAO as

Then, Area OCBAO will be = Area of ODBAO - Area of ODCO

which is equal to

** Question: 4 ** Using integration find the area of region bounded by the triangle whose vertices are and .

** Answer: **

So, we draw BL and CM perpendicular to x-axis.

Then it can be observed in the following figure that,

We have the graph as follows:

Equation of the line segment AB is:

or

Therefore we have Area of

So, the equation of line segment BC is

or

Therefore the area of BLMCB will be,

Equation of the line segment AC is,

or

Therefore the area of AMCA will be,

Therefore, from equations (1), we get

The area of the triangle

** Question:5 ** Using integration find the area of the triangular region whose sides have the equations and .

** Answer: **

The equations of sides of the triangle are .

ON solving these equations, we will get the vertices of the triangle as

Thus it can be seen that,

** Question:6 ** Choose the correct answer.

Smaller area enclosed by the circle and the line is

(A) (B) (C) (D)

** Answer: **

So, the smaller area enclosed by the circle, , and the line, , is represented by the shaded area ACBA as

Thus it can be observed that,

Area of ACBA = Area OACBO - Area of

** Thus, the correct answer is B. **

** Question:7 ** Choose the correct answer.

Area lying between the curves and is

(A) (B) (C) (D)

** Answer: **

The area lying between the curve, and is represented by the shaded area OBAO as

The points of intersection of these curves are and .

So, we draw AC perpendicular to x-axis such that the coordinates of C are (1,0).

Therefore the Area OBAO =

** Thus the correct answer is B. **

**More About NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2**

The NCERT Class 12 Maths chapter application of Integrals mainly deals with the finding out of an area bounded by two curves. Exercise 8.2 Class 12 Maths is an extension of last exercise only. Hence before doing NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 one should complete the exercise 8.1.

**Also Read| **Application of Integrals Class 12 Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2**

The Class 12th Maths chapter 8 exercise has 3 exercises in total maily dealing with the application of integrals.

These Class 12 Maths chapter 8 exercise 8.2 solutions are helpful in solving the questions in the upcoming exercise also.

NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 provides mostly moderate to difficult level of questions.

**Also see-**

NCERT Exemplar Solutions Class 12 Maths Chapter 8

NCERT Solutions for Class 12 Maths Chapter 8

**NCERT Solutions Subject Wise**

NCERT Solutions Class 12 Chemistry

NCERT Solutions for Class 12 Physics

NCERT Solutions for Class 12 Biology

NCERT Solutions for Class 12 Mathematics

**Subject Wise NCERT Exemplar Solutions**

NCERT Exemplar Class 12 Maths

NCERT Exemplar Class 12 Physics

NCERT Exemplar Class 12 Chemistry

NCERT Exemplar Class 12 Biology

Happy learning!!!