NCERT Solutions For Class 12 Maths Chapter 8 – Application Of Integrals Class 12 NCERT Solutions

NCERT Solutions For Class 12 Maths Chapter 8 is designed and prepared by India’s best teachers. This will helps you to clear all the doubts which are raised while in the preparation for the exams. Application Of Integrals Class 12 NCERT Solutions covers multiple exercises and each exercise is provided with a step-by-step explanation for better understanding. However, this chapter will be more useful and helpful for completing your home assignments as well as revision purposes. Class 12 Maths NCERT Solutions plays a prominent role in the preparation of exams. All important topics have been covered in this NCRET Solutions For Class 12 Maths Chapter 8. Professional Teachers give explanations in an easy manner. So you can get a better score in the examination. NCERT Solutions For Class 12 Maths will help the students for CBSE board exams and also for JEE Mains and Advance. Three exercises are given with diagrammatical explanations in the Application Of Integrals Class 12 NCERT Solutions.

NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals

Section No Topic Name
8 Application Of Integrals
8.1 Introduction
8.2 Area Under Simple Curves
8.3 Area Between Two Curves

 

NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 Introduction

Question 1:
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 1



Question 2:
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 2

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Question 3:
Find the area of the region bounded by x2 = 4yy = 2, y = 4 and the y-axis in the first quadrant.
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 3



Question 4:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 4
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 4(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 4(b)



Question 5:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 5
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 5(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 5(b)

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Question 6:

Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 6(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 6(b)



Question 7:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 7
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 7(a)



Question 8:
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 8
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 8(a)



Question 9:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 9
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 9(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 9(b)



Question 10:
Find the area bounded by the curve x2 = 4y and the line x = 4– 2
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 10



Question 11:

Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 11



Question 12:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 12
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 12(a)


Question 13:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 13
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.1 q 13(a)

NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 Area Under Simple Curves

Question 1:
Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 1
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 1(a)



Question 2:
Find the area bounded by curves (x – 1)2 + y2 = 1 and x2 + y 2 = 1
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 2
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 2(a)



Question 3:
Find the area of the region bounded by the curves y = x+ 2, xx = 0 and x = 3
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 3



Question 4:
Using integration find the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3), and (3, 2).
Answer:

BL and CM are drawn perpendicular to x-axis.

It can be observed in the following figure that,

Area (ΔACB) = Area (ALBA) + Area (BLMCB) – Area (AMCA) … (1)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 4
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 4(a)


Question 5:
Using integration find the area of the triangular region whose sides have the equations y = 2x +1, y = 3x + 1 and = 4.
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 5(a)



Question 6:

Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is

A. 2 (π – 2)

B. π – 2

C. 2π – 1

D. 2 (π + 2)
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 6



Question 7:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 7
Answer:
The area lying between the curve, y2 = 4x and y = 2x, is represented by the shaded area OBAO as
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.2 q 7(a)
Thus, the correct answer is B.

NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 Area Between Two Curves

Question 1:

Find the area under the given curves and given lines:

(i) y = x2x = 1, x = 2 and x-axis

(ii) y = x4x = 1, x = 5 and x –axis
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 1
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 1(a)



Question 2:

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

Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 2



Question 3:
Find the area of the region lying in the first quadrant and bounded by y = 4x2x = 0, y = 1, and = 4
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 3



Question 4:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 4
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 4(a)

NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 4(b)



Question 5:
Find the area bounded by the curve y = sin between x = 0 and x = 2π
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 5



Question 6:
Find the area enclosed between the parabola y2 = 4ax and the line y mx
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 6
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 6(a)



Question 7:
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 7
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 7(a)



Question 8:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 8
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 8(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 8(b)



Question 9:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 9
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 9
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 9(b)



Question 10:
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 10


Question 11:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 11
[Hint: the required region is bounded by lines x + y = 1, x – y = 1, – x + y = 1 and – x – = 11] Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 11(a)



Question 12:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 12
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 12(a)


Question 13:
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5), and C (6, 3)
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 13
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 13(a)


Question 14:

Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x – 2y = 6 and x – 3+ 5 = 0
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 14
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 14(a)


Question 15:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 15
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 15(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 15(b)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 15(c)


Question 16:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 16
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 16(a)


Question 17:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 17
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 17(a)


Question 18:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 18
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 18(a)

NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 18(b)


Question 19:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 19
Answer:
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 19(a)
NCERT Solutions For Class 12 Maths Chapter 8 Application Of Integrals Ex 8.3 q 19(b)