# NCERT Solutions for Exercise 8.1 Class 12 Maths Chapter 8 - Application of Integrals

NCERT solutions for Class 12 Maths chapter 8 exercise 8.1 is the extension of last chapter i.e integrals. Concepts learnt in Class 12 Maths NCERT book chapter Integrals will be used heavily in this chapter. Exercise 8. Class 12 Maths deals with area finding of simple curves. NCERT solutions for Class 12 Maths chapter 8 exercise 8.1 requires only basic understanding of integrals which is learnt in the NCERT book previous chapter. Similar questions are asked in Physics also, hence this NCERT syllabus exercise becomes more important. Upcoming exercises are also linked to this exercise, hence sincerely it should be practice. Apart from this below mentioned NCERT exercise can be seen for further topics.

Application of Integrals Exercise 8.2

Application of Integrals Miscellaneous Exercise

**Application of Integrals**** ****C****lass 12 Chapter 8 Exercise: 8.1 **

** Question:1 ** Find the area of the region bounded by the curve and the lines and the -axis in the first quadrant.

** Answer: **

Area of the region bounded by the curve and the lines and the -axis in the first quadrant

Area =

= 14/3 units

** Question:2 ** Find the area of the region bounded by and the -axis in the first quadrant.

** Answer: **

Area of the region bounded by the curve and the -axis in the first quadrant

Area =

units

** Question:3 ** Find the area of the region bounded by and the -axis in the first quadrant.

** Answer: **

The area bounded by the curves and the -axis in the first quadrant is ABCD.

** Question:4 ** Find the area of the region bounded by the ellipse

** Answer: **

The area bounded by the ellipse :

Area will be 4 times the area of EAB.

Therefore,

Therefore the area bounded by the ellipse will be

** Question: 5 ** Find the area of the region bounded by the ellipse

** Answer: **

The area bounded by the ellipse :

The area will be 4 times the area of EAB.

Therefore,

Therefore the area bounded by the ellipse will be

** Question: 6 ** Find the area of the region in the first quadrant enclosed by -axis, line and the circle ** Answer: **

The area of the region bounded by and is ABC shown:

The point B of the intersection of the line and the circle in the first quadrant is .

Area ABC = Area ABM + Area BMC where, M is point in x-axis perpendicular drawn from the line.

Now,area of ** ............(1) **

** and Area of **

** ..................................(2) **

then adding the area (1) and (2), we have then

The Area under ABC

** Question: 7 ** Find the area of the smaller part of the circle cut off by the line

** Answer: **

we need to find the area of smaller part of the circle

Now,

Area of ABCD = 2 X Area of ABC

Area of ABC =

Area of ABCD = 2 X Area of ABC

Therefore, the area of the smaller part of the circle is

** Question:8 ** The area between and is divided into two equal parts by the line , find the value of .

** Answer: **

we can clearly see that given area is symmetrical about x - axis

It is given that

Area of OED = Area of EFCD

Area of OED =

Area of EFCD =

Area of OED = Area of EFCD

Therefore, the value of a is

** Question:9 ** Find the area of the region bounded by the parabola and .

** Answer: **

We can clearly see that given area is symmetrical about y-axis

Therefore,

Area of OCAO = Area of OBDO

Point of intersection of is (1 , 1) and (-1 , 1)

Now,

Area od OCAO = Area OAM - Area of OCMO

Area of OAM =

Area of OCMO =

Therefore,

Area od OCAO

Now,

Area of the region bounded by the parabola and is = 2 X Area od OCAO Units

** Question: 10 ** Find the area bounded by the curve and the line .

** Answer: **

Points of intersections of is

Now,

Area of OBAO = Area of OBCO + Area of OCAO

Area of OBCO = Area of OMBCO- Area of OMBO

Area of OMBCO =

Area of OMBO =

Area of OBCO = Area of OMBCO- Area of OMBO

Similarly,

Area of OCAO = Area of OCALO - Area of OALO

Area of OCALO =

Area of OALO =

Area of OCAO = Area of OCALO - Area of OALO

Now,

Area of OBAO = Area of OBCO + Area of OCAO

Therefore, area bounded by the curve and the line is

** Question: 11 ** Find the area of the region bounded by the curve and the line .

** Answer: **

The combined figure of the curve and

The required are is OABCO, and it is symmetrical about the horizontal axis.

Therefore, Area of OABCO = 2 Area of OAB

therefore the required area is units.

** Question: 12 ** Choose the correct answer in the following

Area lying in the first quadrant and bounded by the circle and the lines and is

** Answer: **

The correct answer is A

The area bounded by circle C(0,0,4) and the line x=2 is

The required area = area of OAB

** Question: 13 ** Choose the correct answer in the following.

Area of the region bounded by the curve , -axis and the line is

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

** Answer: **

The area bounded by the curve and y =3

the required area = OAB =

**More About NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.1**

The NCERT Class 12 Maths chapter Application of Integrals mainly deals with the finding out of area, volume etc. Exercise 8.1 Class 12 Maths is the extension and application of everything learnt in chapter 7. Hence before doing NCERT Solutions for Class 12 Maths chapter 8 exercise 8.1 one should complete chapter 7 Integrals.

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

**Benefits of NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.1**

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 8.1 solutions are helpful in understanding the theory also.

NCERT solutions for Class 12 Maths chapter 8 exercise 8.1 provides some basic questions initially and then moderate to advanced level of questions later on.

**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!!!