Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · NDA · Mathematics · Definite Integration

Definite Integration — NDA Mathematics PYQs

110 previous year questions from Definite Integration with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

110 questionsMathematicsSolutions on every page
1

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(x) g(x) ,dx equal to ?

NDA 2026 Solution View → 2

Passage: Let ₀^ 2 a x+b x (a+b)( x+ x) ,dx=k . Question: What is the value of k ?

NDA 2026 Solution View → 3

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(4-x) g(4-x) ,dx equal to ?

NDA 2026 Solution View → 4

Passage: Let ₀^ 2 a x+b x (a+b)( x+ x) ,dx=k . Question: What is ₀^ 2 a x+b x x+ x ,dx equal to ?

NDA 2026 Solution View → 5

Consider the following for the two (02) items that follow: Let f(x) = [x^2] , where [ ] is the greatest integer function. What is _ 2 ² f(x) , dx equal to?

NDA 2025 Solution View → 6

What is _n^ n+1 (x - [x]) , dx , where [ ] is the greatest integer function and n is a natural number?

NDA 2025 Solution View → 7

If I₁ = _e^ e^2 dx x and I₂ = ₁^2 e^x x , dx , then which one of the following is correct?

NDA 2025 Solution View → 8

Paragraph: Let I = ₀^ 2 f(x) g(x) d x , where f(x)= x and g(x)= x+ x+1 . Question: What is ₀^ 2 d x g(x) equal to?

NDA 2024 Solution View → 9

Paragraph: Let f(t)= (t+ 1+t^2 ) and g(t)= (f(t)) . Question: What is _ - ^ g(t) d t equal to?

NDA 2024 Solution View → 10

Paragraph: Let f(x)= |x^2-x-2 | Question: What is ₀^2 f(x) d x equal to?

NDA 2024 Solution View → 11

What is _ -1 ^1(3 x- 3 x) ^2 x d x equal to?

NDA 2024 Solution View → 12

What is ₀^ 2 a+ x 2 a+ x+ x d x equal to?

NDA 2024 Solution View → 13

Let p= _a^b f(x) d x and q= _a^b|f(x)| d x . If f(x)=e^ -x , then which one of the following is correct?

NDA 2024 Solution View → 14

Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What is ₀^2 h(x) d x equal to?

NDA 2024 Solution View → 15

Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What is _ -1 ^0 h(x) d x equal to?

NDA 2024 Solution View → 16

Let 3 f(x)+f ( 1 x )= 1 x +1 What is 8 ₁^2 f(x) d x equal to?

NDA 2024 Solution View → 17

Let (a)= _a^ a+100 | x| d x What is (a) equal to?

NDA 2024 Solution View → 18

Let (a)= _a^ a+100 | x| d x What is ^ (a) equal to?

NDA 2024 Solution View → 19

Paragraph: Let I = ₀^ 2 f(x) g(x) d x , where f(x)= x and g(x)= x+ x+1 . Question: What is I equal to?

NDA 2024 Solution View → 20

Paragraph: Let f(x)= |x^2-x-2 | Question: What is ₁^3 f(x) d x equal to?

NDA 2024 Solution View → 21

Let I= _ -2 ^ 2 ^4 x+ ^4 x 1+3^x d x What is I equal to?

NDA 2023 Solution View → 22

Let I= _ -2 ^ 2 ^4 x+ ^4 x 1+3^x d x What is ₀^ ( ^4 x+ ^4 x ) d x equal to?

NDA 2023 Solution View → 23

What is ₀^ 8 | x| d x equal to?

NDA 2023 Solution View → 24

Paragraph: Let l= _a^b |x| x d x, a b Question: What is l equal to when a 0 b ?

NDA 2023 Solution View → 25

Paragraph: Let l= _a^b |x| x d x, a b Question: What is l equal to when a b 0 ?

NDA 2023 Solution View → 26

Paragraph: Let I₁= ₀^ x 1+ ^2 x d x and I₂= ₀^ 1 1+ ^2 x d x Question: What is the value of I₂ ?

NDA 2023 Solution View → 27

Paragraph: Let I₁= ₀^ x 1+ ^2 x d x and I₂= ₀^ 1 1+ ^2 x d x Question: What is the value of I₁+I₂ I₁-I₂ ?

NDA 2023 Solution View → 28

Paragraph: Let I₁= ₀^ x 1+ ^2 x d x and I₂= ₀^ 1 1+ ^2 x d x Question: What is the value of 8 I₁^2 ?

NDA 2023 Solution View → 29

What is ₀^1 ( 1 x -1 ) d x equal to?

NDA 2022 Solution View → 30

If ₀^ / 2 ( ^4 x+ ^4 x ) d x=k , then what is the value of ₀^ 20 ( ^4+ ^4 x ) d x ?

NDA 2022 Solution View → 31

What is ₀^ 4 d x ( x+ x)^2 equal to?

NDA 2022 Solution View → 32

What is _ -2 ⁻¹ x |x| d x equal to?

NDA 2022 Solution View → 33

What is _ - / 2 ^ / 2 (e^ x x+e^ x x ) d x equal to?

NDA 2022 Solution View → 34

If f(x)=2^x , then what is ₂¹⁰ f^ (x) f(x) d x equal to?

NDA 2021 Solution View → 35

What is ₀^ 2 e^ ( x) d x equal to?

NDA 2021 Solution View → 36

What is ₀^ ( x 2 ) d x equal to?

NDA 2021 Solution View → 37

What is ₀^a f(a-x) f(x)+f(a-x) d x equal to?

NDA 2021 Solution View → 38

If ₀^a[f(x)+f(-x)] d x= _ -a ^a g(x) d x then what is g(x) equal to?

NDA 2021 Solution View → 39

If f(x) satisfies f( l )=f(4) , then what is ₁^4 f^ (x) d x equal to?

NDA 2021 Solution View → 40

If _ -2 ^0 f(x) d x=k , then _ -2 ^0|f(x)| d x is

NDA 2021 Solution View → 41

What is the value of ₀^ / 4 ( ^3 x+ x ) d x ?

NDA 2020 Solution View → 42

Paragraph: Consider the integrals I ₁= ₀^x x d x 1+ x and I ₂= ₀^ ( -x) d x 1- ( +x) Question: What is the value of I₁ ?

NDA 2019 Solution View → 43

₀^ 2 | x- x| d x is equal to

NDA 2019 Solution View → 44

₀^ 2 e^ x x d x is equal to

NDA 2019 Solution View → 45

Paragraph: Consider the integrals I ₁= ₀^x x d x 1+ x and I ₂= ₀^ ( -x) d x 1- ( +x) Question: What is the value of I ₁+ I ₂ ?

NDA 2019 Solution View → 46

What is _a^b[x] d x+ _a^b[-x] d x equal to, where[.] is the greatest integer function?

NDA 2018 Solution View → 47

What is ₂^8|x-5| d x equal to?

NDA 2018 Solution View → 48

What is _ -1 ^1 d d x ( ⁻¹ 1 x ) d x equal to?

NDA 2018 Solution View → 49

What is ₀^ e ^ x x d x equal to?

NDA 2018 Solution View → 50

What is ₁^ e x x dx equal to?

NDA 2018 Solution View → 51

What is ₀^ 2 [x^2 ] d x equal to (where [.] is the greatest integer function)?

NDA 2018 Solution View → 52

What is the value of _ - 4 ^ 4 ( x - x) d x ?

NDA 2018 Solution View → 53

If _a^b x^3 d x=0 and _a^b x^2 d x= 2 3 , then what are the values of a and b respectively?

NDA 2018 Solution View → 54

What is ₀^1 x(1-x)^9 d x equal to?

NDA 2018 Solution View → 55

What is ₀^ 2 d 1+ equal to?

NDA 2017 Solution View → 56

What is ₀^ 2 1+ x 2 d x equal to?

NDA 2017 Solution View → 57

If f( x ) and g ( x ) are continuous functions satisfying f( x )=f( a - x ) and g ( x )+ g ( a - x )=2 , then what is ₀^ a f( x ) g ( x ) dx equal to?

NDA 2017 Solution View → 58

The value of ₀^ 4 x d x+ ₀^ 4 x d x is equal to

NDA 2017 Solution View → 59

What is _ e ⁻¹ ^ e ^2 | x x | dx equal to?

NDA 2017 Solution View → 60

If ₀^ / 2 dx 3 x +5 = k ⁻¹ ⁻¹ 2 , then what is the value of K ?

NDA 2016 Solution View → 61

Let f(x) be a function such that f^ ( 1 x )+x^3 f^ (x)=0 , What is _ -1 ^1 f(x) d x equal to?

NDA 2016 Solution View → 62

What is ₁^3 |1- x ^4 | dx equal to?

NDA 2016 Solution View → 63

Consider the functions f(x)=x g(x) and g(x)= [ 1 x ] Where [ ] is the greatest integer function. What is _ 1 3 ^ 1 2 g(x) d x equal to?

NDA 2016 Solution View → 64

Given that a _ n = ₀^ ^2 ( n +1) x 2 x dx What is a_ n-1 -a_ n-4 equal to ?

NDA 2016 Solution View → 65

Consider the functions f(x)=x g(x) and g(x)= [ 1 x ] Where [ ] is the greatest integer function. What is _ 1 3 ^1 f(x) d x equal to ?

NDA 2016 Solution View → 66

Given that a _ n = ₀^ ^2 ( n +1) x 2 x dx Consider the following statements: 1. The sequence a_ 2 n is in AP with common difference zero. 2. The sequence a _ 2 n +1 is in AP with c

NDA 2016 Solution View → 67

If _ -2 ^5 f(x) d x=4 and ₀^5 1+f(x) d x=7 , then what is _ -2 ^0 f(x) d x equal to?

NDA 2016 Solution View → 68

What is ₀^ 4 | x | dx equal to?

NDA 2016 Solution View → 69

What is _ -2 ^2 x d x- _ -2 ^2[x] d x equal to, where [ ] is the greatest integer function?

NDA 2016 Solution View → 70

The value of _a^b x^7+ x x d x where a+b=0 is

NDA 2015 Solution View → 71

Consider the integrals A= ₀^ x d x x+ x and B= ₀^ x d x x- x Which one of the following is correct?

NDA 2015 Solution View → 72

If 0 a b , then _a^b |x| x d x is equal to

NDA 2015 Solution View → 73

Consider the integrals A= ₀^ x d x x+ x and B= ₀^ x d x x- x What is the value of B ?

NDA 2015 Solution View → 74

Consider the integral I_m= ₀^ 2 m x x d x , where m is a positive integer. . Consider the following: 1. I_m-I_ m-1 is equal to 0 . 2. I_ 2 m I_m Which of the above is/are correct?

NDA 2015 Solution View → 75

Consider the integral I_m= ₀^ 2 m x x d x , where m is a positive integer. What is I_m equal to?

NDA 2015 Solution View → 76

_ -1 ^1 x | x | dx is equal to

NDA 2015 Solution View → 77

₀^ 2 ^5 ( x 4 ) d x is equal to

NDA 2015 Solution View → 78

Consider the integral I_m= ₀^ 2 m x x d x , where m is a positive integer. What is I ₁ equal to?

NDA 2015 Solution View → 79

Consider the integral I_m= ₀^ 2 m x x d x , where m is a positive integer. What is I₂+I₃ equal to?

NDA 2015 Solution View → 80

What is ₀^ 2 d x a^2 ^2 x+b^2 ^2 x equal to?

NDA 2014 Solution View → 81

Consider I = ₀^ x d x 1+ x What is I equal to?

NDA 2014 Solution View → 82

Consider I = ₀^ x d x 1+ x What is ₀^ ( -x) d x 1+ x equal to?

NDA 2014 Solution View → 83

Consider I = ₀^ x d x 1+ x What is ₀^ d x 1+ x equal to?

NDA 2014 Solution View → 84

Consider the integral I = ₀^ ( x) d x What is ₀^ / 2 ( x) d x equal to?

NDA 2014 Solution View → 85

Consider the integral I = ₀^ ( x) d x What is ₀^ / 2 ( x) d x equal to?

NDA 2014 Solution View → 86

What is ₀^1 e^ ⁻¹ x d x 1+x^2 equal to?

NDA 2014 Solution View → 87

Paragraph : Consider the integrals I ₁= _ 6 ^ 3 d x 1+ x and I ₂= _ 6 ^ 3 x d x x + x . Question : What is I ₁- I ₂ equal to?

NDA 2014 Solution View → 88

What is _ - 2 ^ 2 x x d x equal to?

NDA 2014 Solution View → 89

What is ₀^ 2 ( x) d x equal to?

NDA 2014 Solution View → 90

Paragraph : Consider the integrals I ₁= _ 6 ^ 3 d x 1+ x and I ₂= _ 6 ^ 3 x d x x + x . Question : What is I ₁ equal to?

NDA 2014 Solution View → 91

What is ₁^2 x d x equal to?

NDA 2013 Solution View → 92

What is ₀^1 x e^x d x equal to?

NDA 2013 Solution View → 93

What is _ 6 ^ 6 ^5 x ^3 x x^4 d x is equal to?

NDA 2013 Solution View → 94

What is ₀^2 d x x^2+4 equal to?

NDA 2013 Solution View → 95

What is ₀^2 e^ x d x equal to?

NDA 2013 Solution View → 96

What is _ -a ^a (x^3+ x ) d x equal to?

NDA 2013 Solution View → 97

What is _ -1 ^1 x|x| d x equal to?

NDA 2012 Solution View → 98

What is ₀^1 ⁻¹ x 1+x^2 d x equal to?

NDA 2012 Solution View → 99

What is _ - 2 ^ 2 | x| d x equal to?

NDA 2012 Solution View → 100

What is ₀^ / 2 2 x ( x) d x equal to?

NDA 2012 Solution View → 101

What is ₀^1 ⁻¹ x 1+x^2 d x equal to?

NDA 2012 Solution View → 102

If f(x) is an even function, then what is ₀^ f( x) d x equal to?

NDA 2011 Solution View → 103

What is ₀^ d x 1+2 ^2 x equal to?

NDA 2011 Solution View → 104

If I_n= ₀^ 4 ^n x d x then what is I_n+I_ n-2 equal to?

NDA 2011 Solution View → 105

If ₁^2 k^2+(4-4 k) x+4 x^3 d x 12 , then which one of the following is correct?

NDA 2011 Solution View → 106

What is the value of _ / 6 ^ / 4 d x x x ?

NDA 2010 Solution View → 107

What is the value of the integral _ -1 ^1|x| d x

NDA 2010 Solution View → 108

What is the value of ₁^2 e^x ( 1 x - 1 x^2 ) d x

NDA 2010 Solution View → 109

What is _ - 4 ^ 4 ^3 x d x equal to?

NDA 2010 Solution View → 110

What is ₀^ / 2 ^2 x ^3 x+ ^3 x d x ?

NDA 2010 Solution View →
Practice all Definite Integration questions in the app →