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Test: Application of Integrals- 2 - JEE MCQ


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25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Application of Integrals- 2

Test: Application of Integrals- 2 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Application of Integrals- 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Application of Integrals- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Application of Integrals- 2 below.
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Test: Application of Integrals- 2 - Question 1

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

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Required area :

Test: Application of Integrals- 2 - Question 2

Area bounded by the curves satisfying the conditions  is given by

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Test: Application of Integrals- 2 - Question 3

The area of the figure bounded by y = ex, y = e−x and the straight line x = 1 is

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Test: Application of Integrals- 2 - Question 4

The area bounded by the parabolas y = (x+1)2 and y = (x−1)2 and the line y = (1/4) is equal to

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Required area :

Test: Application of Integrals- 2 - Question 5

The area enclosed between the curve y = loge(x+e) and x = loge 1/y and the x- axes is

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Required area is :


Test: Application of Integrals- 2 - Question 6

The area bounded by the curve y = x3, the x – axis and two ordinates x = 1 and x = 2 is

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Test: Application of Integrals- 2 - Question 7

The area bounded by the parabola y = x2 + 1 and the straight line x + y = 3 is given by

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The two curves parabola and the line meet where,

Required area ;

Test: Application of Integrals- 2 - Question 8

The area enclosed between the curves y = √x  , x = 2y+3and the x-axis is

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The two curves meet where;

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

Test: Application of Integrals- 2 - Question 9

The area of the region {(x , y) : x2+y2⩽1⩽x+y} is equal to

Detailed Solution for Test: Application of Integrals- 2 - 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- 2 - Question 10

The area bounded by y = |sinx| , the x – axis and the line |x| = π is

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Required area :

Test: Application of Integrals- 2 - Question 11

If A is the area between the curve y = sin2x , x – axis and the lines x = 

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Required area :


Test: Application of Integrals- 2 - Question 12

The area bounded by the curves y2 = x and y = x2 is

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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- 2 - Question 13

The positive value of the parameter a for which the area of the figure bounded by y = sin ax , y = 0 , x = x/a and x = x/3a is 3 is equal to

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We have :

Test: Application of Integrals- 2 - Question 14

The area bounded by the parabolas y = 5x2and y − 9 = 2x2 is

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Required area : 


Test: Application of Integrals- 2 - Question 15

The area bounded by the curves y = √x , 2y+3 = x and the x – axis in the first quadrant is

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Required area :

Test: Application of Integrals- 2 - Question 16

The area bounded by y = 2cosx , x = 0 to x = 2π and the axis of x in square units is

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Required area :


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

Test: Application of Integrals- 2 - Question 17

The area common to the circle x2+y2 = 16a2 and the parabola y2 = 6ax is 

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Required area :



Test: Application of Integrals- 2 - Question 18

The area bounded by the parabola y2 = 4x and the line x + y = 3 is

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Required area :

Test: Application of Integrals- 2 - Question 19

The area enclosed by the parabola y2 = 2x and its tangents through the point (-2 , 0) is

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Test: Application of Integrals- 2 - Question 20

The area bounded by the curve y = x log x and  y = 2x−2x2 is

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Required area :

Test: Application of Integrals- 2 - Question 21

The area of the figure bounded by the curve y = logex , the x – axis and the straight line x = e is

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Required area :

Test: Application of Integrals- 2 - Question 22

The area of the region bounded by the curves y = |x−1| and y = 3 - |x| is

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Required area :

Test: Application of Integrals- 2 - Question 23

The area bounded by the curve y = x2+1and the line x + y = 3 is

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The two curves parabola and the line meet where,

Therefore , the required area is :

Test: Application of Integrals- 2 - Question 24

The area bounded by the angle bisectors of the lines x2−y2+2y = 1 and x+y = 3 is

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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- 2 - Question 25

The area bounded by the curves y= |x−1| and y = 1 is given by

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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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