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Indefinite Integration — NDA Mathematics PYQs

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

77 questionsMathematicsSolutions on every page
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Passage: Let ,d (2+ )(3+4 ) =A |2+ |+B |3+4 | . Question: What is the value of A ?

NDA 2026 Solution View → 2

Passage: Let ,d (2+ )(3+4 ) =A |2+ |+B |3+4 | . Question: What is the value of B ?

NDA 2026 Solution View → 3

What is dx 10^x + 10^ -x equal to?

NDA 2025 Solution View → 4

Consider the following for the two (02) items that follow: Let the function y = (1 - x)⁻¹ , where x 2n and n is an integer. What is y , dx equal to?

NDA 2025 Solution View → 5

For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . Consider the following: I. du dx = -v II. dv dx = -u Which of the above is/are correct?

NDA 2025 Solution View → 6

For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . What is u + v equal to?

NDA 2025 Solution View → 7

Let d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c What is the value of ?

NDA 2024 Solution View → 8

Paragraph: Let 2 x^2-1 x^2+1 d x= U (x) V (x)-3 U (x)+ V (x) +c Question: What is U (x) V (x) equal to?

NDA 2024 Solution View → 9

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

NDA 2024 Solution View → 10

Given that 3 x+4 x 2 x+5 x d x= x 29 + 29 |2 x+5 x|+c What is the value of ?

NDA 2024 Solution View → 11

Given that 3 x+4 x 2 x+5 x d x= x 29 + 29 |2 x+5 x|+c What is the value of ?

NDA 2024 Solution View → 12

Let d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c What is the value of ?

NDA 2024 Solution View → 13

Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further f(0)=6, f^ ( 3)=282 and ₀^ 2 f(x) d x=11 Question: What is the value of R ?

NDA 2023 Solution View → 14

Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further f(0)=6, f^ ( 3)=282 and ₀^ 2 f(x) d x=11 Question: What is the value of Q ?

NDA 2023 Solution View → 15

What is (x^x )^2(1+ x) d x equal to?

NDA 2022 Solution View → 16

What is e^ x (1+ x+x x) d x equal to?

NDA 2022 Solution View → 17

If I₁= e^x d x e^x+e^ -x and I₂= d x e^ 2 x +1 , then what is I₁+I₂ equal to?

NDA 2022 Solution View → 18

What is ( x)^ 1.5 -( x)^ 1.5 x x d x equal to?

NDA 2022 Solution View → 19

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

NDA 2022 Solution View → 20

What is d x x (x^2+1 ) equal to?

NDA 2021 Solution View → 21

What is the integral of f(x)=1+x^2+x^4 with respect to x^2 ?

NDA 2021 Solution View → 22

What is d x x+ x equal to ?

NDA 2021 Solution View → 23

If 1- 2 x d x=A x+B x+C , where 0 x 4 , then which one of the following is correct?

NDA 2021 Solution View → 24

What is d x ^2 ( ⁻¹ x ) equal to ?

NDA 2021 Solution View → 25

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

NDA 2021 Solution View → 26

If p(x)=(4 e)^ 2 x , then what is p(x) d x equal to?

NDA 2020 Solution View → 27

What is (e^ x + x ) x d x equal to ?

NDA 2020 Solution View → 28

What is d x x (x^n+1 ) equal to?

NDA 2020 Solution View → 29

What is the value of k such that integration of 3 x^2+8-4 k x with respect to x , may be a rational function?

NDA 2020 Solution View → 30

What is d x x(1+ x)^n equal to (n^1 1 ) ?

NDA 2019 Solution View → 31

What is d x 2 x^2-2 x+1 equal to?

NDA 2019 Solution View → 32

What is e^ x (a) d x equal to ?

NDA 2019 Solution View → 33

What is (x^2 ) d x equal to ?

NDA 2019 Solution View → 34

What is ^3 x x d x equal to? Where c is the constant o integration.

NDA 2018 Solution View → 35

What is e^ In ( x) d x equal to? Where c is the constant of integration.

NDA 2018 Solution View → 36

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

NDA 2018 Solution View → 37

What is dx 2^ x -1 equal to?

NDA 2018 Solution View → 38

What is dx x ( x ^7+1 ) equal to?

NDA 2017 Solution View → 39

What is ( x ^ e -1 + e ^ x -1 ) dx x ^ e + e ^ x equal to?

NDA 2017 Solution View → 40

Let f( x ) be an indefinite integral of ^2 x . Consider the following statements : Statement 1 : The function f( x ) satisfies f( x + )=f( x ) for all real x . Statement 2: ^2(x+ )

NDA 2017 Solution View → 41

What is ⁻¹( x+ x) d x equal to?

NDA 2017 Solution View → 42

( In x)⁻¹ d x- ( In x)⁻² d x is equal to

NDA 2017 Solution View → 43

What is x^4-1 x^2 x^4+x^2+1 d x equal to?

NDA 2016 Solution View → 44

What is e^ x x ^3 x- x ^2 x d x equal to?

NDA 2016 Solution View → 45

Consider the function f ( x )=( x -1)^2( x +1)( x -2)^3 . Let f(x) and g(x) be twice differentiable functions on [0,2] satisfying f ^ ( x )= g ^ ( x ), f ^ (1)=4, ~g ^ (1)=6, f(2)=

NDA 2016 Solution View → 46

dx 1+ e ^ - x is equal to where c is the constant of integration

NDA 2015 Solution View → 47

The integral d x a x+b x is of the form 1 r In [ ( x+ 2 ) ] . What is r equal to?

NDA 2015 Solution View → 48

What is d x x^2+a^2 equal to? where c is the constant of integration.

NDA 2015 Solution View → 49

The integral d x a x+b x is of the form 1 r In [ ( x+ 2 ) ] . What is equal to?

NDA 2015 Solution View → 50

What is x e^x d x (x+1)^2 equal to? where c is the constant integration.

NDA 2015 Solution View → 51

Consider the function f^ (x)= ^4 x+4 with f(0)=0 and f^ (0)=0 . What is f^ (x) equal to?

NDA 2014 Solution View → 52

Consider the function f^ (x)= ^4 x+4 with f(0)=0 and f^ (0)=0 . What is f(x) equal to?

NDA 2014 Solution View → 53

Consider x ⁻¹ x d x= A (x^2+1 ) ⁻¹ x+ B x+ C , where C is the constant of integration. What is the value of A ?

NDA 2014 Solution View → 54

Consider x ⁻¹ x d x= A (x^2+1 ) ⁻¹ x+ B x+ C , where C is the constant of integration. What is the value of B?

NDA 2014 Solution View → 55

What is d x 4+x^2 equal to? where c is an arbitrary constant.

NDA 2013 Solution View → 56

What is (x x+ x) d x equal to? where c is an arbitrary constant.

NDA 2013 Solution View → 57

What is ^2 x d x+ ^2 x d x equal to? where c is an arbitrary constant.

NDA 2013 Solution View → 58

What is e^ e^x e^x d x equal to? where c is an arbitrary constant.

NDA 2013 Solution View → 59

What is e^ x d x equal to? where c is constant of integration.

NDA 2013 Solution View → 60

What is d x x x equal to ? where c is the constant of integration.

NDA 2013 Solution View → 61

What is a^x e^x d x equal to?

NDA 2012 Solution View → 62

What is x x d x equal to?

NDA 2012 Solution View → 63

What is (x^2+1 )^ 5 2 x d x equal to?

NDA 2012 Solution View → 64

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

NDA 2012 Solution View → 65

Consider the following: 1. 10 d x=x+c 2. 10^x d x=10^x+c where c is the constant of integration. Which of the above is/are correct?

NDA 2012 Solution View → 66

What is d x ^2 x ^2 x equal to? where c is the constant of integration.

NDA 2011 Solution View → 67

What is x x d x equal to? where c is a constant of integration.

NDA 2011 Solution View → 68

What is e^x ( x + 1 2 x ) d x equal to? Where c is a constant of integration.

NDA 2011 Solution View → 69

What is ⁻¹( x) d x equal to? where k is a constant of integration.

NDA 2011 Solution View → 70

What is equal to? e^x(1+x) ^2 (x e^x ) d x where c is a constant of integration.

NDA 2010 Solution View → 71

What is ^n x x d x equal to? where c is a constant of integration.

NDA 2010 Solution View → 72

If x^2 x d x= x^2 m x+ x^3 n +c , then what are the values of m and n respectively? where c is a constant of integration.

NDA 2010 Solution View → 73

What is 1 1+e^x d x equal to? where c is constant of integration.

NDA 2010 Solution View → 74

What is e^ x x d x equal to? where c is a constant of integration.

NDA 2010 Solution View → 75

What is x^4+1 x^2+1 d x equal to? where c is a constant of integration.

NDA 2010 Solution View → 76

Consider the following statements: I. Every function has a primitive. II. A primitive of a function is unique. Which of the statements given above is/are correct?

NDA 2010 Solution View → 77

What is x e^ x d x equal to? where c is a constant of integration.

NDA 2010 Solution View →
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