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JEE Exam  >  JEE Test  >  Chapter-wise Tests Main & Advanced  >  Test: Application of Integrals- 6 - JEE MCQ

Application of Integrals- 6 - Free MCQ Practice Test with solutions, JEE


MCQ Practice Test & Solutions: Test: Application of Integrals- 6 (25 Questions)

You can prepare effectively for JEE Chapter-wise Tests for JEE Main & Advanced with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Application of Integrals- 6". These 25 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 25 minutes
  • - Number of Questions: 25

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Test: Application of Integrals- 6 - Question 1
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The area lying in the first quadrant and bounded by the curve y = x3 , the x – axis and the ordinates at x = - 2 and x = 1 is

Detailed Solution: Question 1

Required area :

Test: Application of Integrals- 6 - Question 2
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Area bounded by the curves satisfying the conditions  is given by

Detailed Solution: Question 2



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Test: Application of Integrals- 6 - Question 3
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The area of the figure bounded by y = ex, y = e−x and the straight line x = 1 is

Detailed Solution: Question 3

Test: Application of Integrals- 6 - Question 4
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The area bounded by the parabolas y = (x+1)2 and y = (x−1)2 and the line y = (1/4) is equal to

Detailed Solution: Question 4

Required area :

Test: Application of Integrals- 6 - Question 5
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The area enclosed between the curve y = loge(x+e) and x = loge 1/y and the x- axes is

Detailed Solution: Question 5

Required area is :


Test: Application of Integrals- 6 - Question 6
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The area bounded by the curve y = x3, the x – axis and two ordinates x = 1 and x = 2 is

Detailed Solution: Question 6


Test: Application of Integrals- 6 - Question 7
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The area bounded by the parabola y = x2 + 1 and the straight line x + y = 3 is given by

Detailed Solution: Question 7

The two curves parabola and the line meet where,

Required area ;

Test: Application of Integrals- 6 - Question 8
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The area enclosed between the curves y = √x  , x = 2y+3and the x-axis is

Detailed Solution: Question 8

 

The two curves meet where;

Therefore, the two curves meet where x = 9.
Therefore,required Area:

Test: Application of Integrals- 6 - Question 9
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The area of the region {(x , y) : x2+y2⩽1⩽x+y} is equal to

Detailed Solution: Question 9

x2+y2 = 1,x+y = 1
Meets when 
x2(1−x)2 = 1
⇒ x2+1+x2−2x = 1
⇒ 2x2−2x= 0 ⇒ 2x(x−1)=0
⇒ x = 0,x = 1.
i.e. points (1 ,0) ,(0 ,1). Therefore , required area is ;

Test: Application of Integrals- 6 - Question 10
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The area bounded by y = |sinx| , the x – axis and the line |x| = π is

Detailed Solution: Question 10

Required area :

Test: Application of Integrals- 6 - Question 11
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If A is the area between the curve y = sin2x , x – axis and the lines x = 

Detailed Solution: Question 11

Required area :


Test: Application of Integrals- 6 - Question 12
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The area bounded by the curves y2 = x and y = x2 is

Detailed Solution: Question 12

The two curves meet in (0 , 0) and (1, 1).The required area lies above the curve y = x2 and below x = y2 and is equal to ;

Test: Application of Integrals- 6 - Question 13
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The positive value of the parameter a for which the area of the figure bounded by y = sin ax, y = π/a, and y = π/3a is 3 is equal to

Detailed Solution: Question 13

We have :

Test: Application of Integrals- 6 - Question 14
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The area bounded by the parabolas y = 5x2and y − 9 = 2x2 is

Detailed Solution: Question 14

Required area : 


Test: Application of Integrals- 6 - Question 15
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The area bounded by the curves y = √x , 2y+3 = x and the x – axis in the first quadrant is

Detailed Solution: Question 15

Required area :

Test: Application of Integrals- 6 - Question 16
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The area bounded by y = 2cosx , x = 0 to x = 2π and the axis of x in square units is

Detailed Solution: Question 16

Required area :


Therefore , total area from x = 0 to x = 2π is 4 X 2= 8 sq. units.

Test: Application of Integrals- 6 - Question 17
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The area common to the circle x2+y2 = 16a2 and the parabola y2 = 6ax is 

Detailed Solution: Question 17

Required area :



Test: Application of Integrals- 6 - Question 18
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The area bounded by the parabola y2 = 4x and the line x + y = 3 is

Detailed Solution: Question 18

Required area :

Test: Application of Integrals- 6 - Question 19
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The area enclosed by the parabola y2 = 2x and its tangents through the point (-2 , 0) is

Detailed Solution: Question 19


Test: Application of Integrals- 6 - Question 20
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The area bounded by the curve y = x log x and  y = 2x−2x2 is

Detailed Solution: Question 20

Required area :

Test: Application of Integrals- 6 - Question 21
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The area of the figure bounded by the curve y = logex , the x – axis and the straight line x = e is

Detailed Solution: Question 21

Required area :

Test: Application of Integrals- 6 - Question 22
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The area of the region bounded by the curves y = |x−1| and y = 3 - |x| is

Detailed Solution: Question 22

Required area :

Test: Application of Integrals- 6 - Question 23
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The area bounded by the curve y = x2+1and the line x + y = 3 is

Detailed Solution: Question 23

The two curves parabola and the line meet where,

Therefore , the required area is :

Test: Application of Integrals- 6 - Question 24
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The area bounded by the angle bisectors of the lines x2−y2+2y = 1 and x+y = 3 is

Detailed Solution: Question 24

The angle bisectors of the line given by x2−− y2+2y = 1 are x = 0 , y = 1. Required area = 1/2 .2.2 = 2 sq. units

Test: Application of Integrals- 6 - Question 25
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The area bounded by the curves y= |x−1| and y = 1 is given by

Detailed Solution: Question 25

The given curves are : (i) y = x – 1 , x > 1 . (ii) y = - (x – 1) , x < 1. (iii) y = 1 these three lines enclose a triangle whose area is : 1/2 .base.height = 1/2 .2 .1 = 1 sq. unit.

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About this JEE Practice Test

This test contains 25 MCQs on Application of Integrals- 6 with detailed solutions for each question. It is part of the Chapter-wise Tests for JEE Main & Advanced course on EduRev, designed to align with the current JEE syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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