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Definite Integration — JEE Main & Advanced Mathematics PYQs

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

692 questionsMathematicsSolutions on every page
1

The value of the definite integral ₀² 1 3^ x+3 2 , dx is

JEE Advanced 2026 Solution View → 2

The value of the integral ₀² x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) , dx is equal to:

JEE Main 2026 Solution View → 3

If _ /6 ^ /4 ( (x- 3 ) (x+ 3 )+1 )dx = _e( 3 -1) , then 9 ^2 is equal to ________.

JEE Main 2026 Solution View → 4

Let A = bmatrix 1 & 3 & -1 2 & 1 & 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) = ₀^x (t^2 + 2t + 3) ,dt , x [1, ] . If M and m are respectively the maximum and the minimum va

JEE Main 2026 Solution View → 5

Let f: R R be such that f(xy) = f(x)f(y) , for all x, y R and f(0) 0 . Let g: [1, ) R be a differentiable function such that x^2 g(x) = ₁^x (t^2 f(t) - tg(t)) ,dt . Then g(2) is eq

JEE Main 2026 Solution View → 6

The value of the integral _ -1 ¹ ( x^3 + |x| + 1 x^2 + 2|x| + 1 ) dx is equal to :

JEE Main 2026 Solution View → 7

The value of the integral _ - /4 ^ /4 ( 32 ^4 x 1 + e^ x )dx is:

JEE Main 2026 Solution View → 8

Let (2^ 1-a + 2^ 1+a ) , f(a) , (3^a + 3^ -a ) be in A.P. and be the minimum value of f(a) . Then the value of the integral _ _e( -1) ^ _e( ) dx (e^ 2x - e^ -2x ) is :

JEE Main 2026 Solution View → 9

Let f: [1, ) R be a differentiable function defined as f(x) = ₁^x f(t) ,dt + (1-x)( _e x - 1) + e . Then the value of f(f(1)) is :

JEE Main 2026 Solution View → 10

The value of the integral ₀^ _e(x) x^2 + 4 ,dx is:

JEE Main 2026 Solution View → 11

The value of the integral _ /6 ^ /3 ( 4 - ^2 x ^4 x ) dx is:

JEE Main 2026 Solution View → 12

The integral ₀¹ ⁻¹(1+x+x^2)dx is equal to:

JEE Main 2026 Solution View → 13

Let f be a twice differentiable function such that f(x)= ₀^ x (t-x)dt- ₀^ x f(t) t ,dt , x (- 2 , 2 ) . Then f'' ( 6 )+12f' (- 6 )+f ( 6 ) is equal to ______

JEE Main 2026 Solution View → 14

Let _ -2 ² (| x| + [x x]) ,dx = 2(3 - 2) + , where [ ] is the greatest integer function. Then ( 2 ) equals:

JEE Main 2026 Solution View → 15

The value of ₀^ 20 ( ^4 x + ^4 x) , dx is equal to:

JEE Main 2026 Solution View → 16

Let [ ] denote the greatest integer function. Then the value of ₀^3 ( e^x + e^ -x [x]! ) dx is :

JEE Main 2026 Solution View → 17

If = ₀^ 2 3 ₂(x^2 + 4) ,dx + ₂^4 2^x - 4 ,dx , then ^2 is equal to _______.

JEE Main 2026 Solution View → 18

Let [ ] denote the greatest integer function. Then _ - 2 ^ 2 ( 12(3+[x]) 3+[ x]+[ x] ) d x is equal to :

JEE Main 2026 Solution View → 19

Let f be a polynomial function such that f (x²+1 )=x⁴+5 x²+2 , for all x R . Then ₀³ f(x) d x is equal to

JEE Main 2026 Solution View → 20

If ( 1-5 ² x ⁵ x ² x ) d x=f(x)+ C , where C is the constant of integration, then f ( 6 )-f ( 4 ) is equal to

JEE Main 2026 Solution View → 21

The value of _ r=1 ²⁰ ( | ( ₀^ r x| x| d x ) | ) is _ _ _ _

JEE Main 2026 Solution View → 22

If f(x) satisfies the relation f(x)=e^ x + ₀¹ (y+x e^ x ) f(y) d y , then e+f(0) is equal to _ _ _ _ .

JEE Main 2026 Solution View → 23

Let a differentiable function f satisfy the equation ₀³⁶ f ( t x 36 ) d t=4 f(x) . If y=f(x) is a standard parabola passing through the points (2,1) and (-4, ) , then ^ is equal to

JEE Main 2026 Solution View → 24

The number of elements in the set S = x: x [0,100] . and . ₀^ x t² (x-t) d t=x² is _ _ _ _ .

JEE Main 2026 Solution View → 25

The value of the integral _ 24 ^ 5 24 ~d x 1+ [3] 2 x is :

JEE Main 2026 Solution View → 26

Let f(x)=[x]²-[x+3]-3, x R , where [] is the greatest integer funtion. Then

JEE Main 2026 Solution View → 27

Let [ ] be the greatest integer function. If = ₀⁶⁴ (x^ 1 / 3 - [x^ 1 / 3 ] ) d x , then 1 ₀^ ( ² ⁶ + ⁶ ) d is equal to _ _ _ _ .

JEE Main 2026 Solution View → 28

The value of _ - 2 ^ 2 ( 1 [x]+4 ) d x , where [ ] denotes the greatest integer function, is

JEE Main 2026 Solution View → 29

If ₀¹ 4 ⁻¹ (1-2 x+4 x² ) d x= atan ⁻¹(2)- blog _ e (5) , where a , b N , then (2 a + b ) is equal to _ _ _ _ .

JEE Main 2026 Solution View → 30

The value of _ - / 6 ^ / 6 ( +4 x¹¹ 1- (|x|+ / 6) ) d x is equal to:

JEE Main 2026 Solution View → 31

6 ₀^ |( 3 x+ 2 x+ x)| d x is equal to _ _ _ _ .

JEE Main 2026 Solution View → 32

If = _ 1 2 ^2 ⁻¹ x 2 x^2-3 x+2 d x then the value of 7 ( 2 7 ) is ____________. (Here, the inverse trigonometric function ⁻¹ x assumes values in (- 2 , 2 ) .)

JEE Advanced 2025 Solution View → 33

Let f(x) be a positive function and I₁= _ - 1 2 ^1 2 x f(2 x(1-2 x)) d x and I₂= _ -1 ^2 f(x(1-x)) d x . Then the value of I₂ I₁ is equal to ________

JEE Main 2025 Solution View → 34

The integral _ -1 ^ 3 2 ( | ^2 x ( x) | ) d x is equal to:

JEE Main 2025 Solution View → 35

The integral ₀^ (x+3) x 1+3 ^2 x d x is equal to :

JEE Main 2025 Solution View → 36

The value of _ -1 ^1 (1+ |x|-x ) e^x+( |x|-x ) e^ -x e^x+e^ -x d x is equal to

JEE Main 2025 Solution View → 37

The integral ₀^ 8 x d x 4 ^2 x+ ^2 x is equal to

JEE Main 2025 Solution View → 38

Let the domain of the function f( x )= ₂ ₄ ₆ (3+4 x-x^2 ) be ( a , ~b ) . If ₀^ b - a [ x ^2 ] dx = p - q - r , p , q , r N , gcd ( p , q , r )=1, where [ ] is the greatest integer

JEE Main 2025 Solution View → 39

Let (a, b) be the point of intersection of the curve x^2=2 y and the straight line y-2 x-6=0 in the second quadrant. Then the integral I= _a^b 9 x^2 1+5^x d x is equal to :

JEE Main 2025 Solution View → 40

4 ₀^1 ( 1 3+x^2 + 1+x^2 ) d x-3 _e( 3 ) is equal to :

JEE Main 2025 Solution View → 41

Let [.] denote the greatest integer function. If ₀^ e^3 [ 1 e ^ x -1 ] dx = - _ e 2 , then ^3 is equal to _______ .

JEE Main 2025 Solution View → 42

Let f(x)= ₀^t t (t^2-9 t+20 ) d t, 1 x 5 . If the range of f is [ , ] , then 4( + ) equals :

JEE Main 2025 Solution View → 43

If 24 ₀^ 4 ( |4 x- 12 |+[2 x] ) d x=2 + , where [ ] denotes the greatest integer function, then is equal to _______.

JEE Main 2025 Solution View → 44

The integral (80 ₀^ 4 ( + 9+16 2 ) d ) is equal to :

JEE Main 2025 Solution View → 45

Let (f:(0, ) R ) be a twice differentiable function. If for some ( a 0, ₀^1 f( x) d = a f(x), f(1)=1 ) and (f(16)= 1 8 ), then (16-f^ ( 1 16 ) ) is equal to _______.

JEE Main 2025 Solution View → 46

Let f be a real valued continuous function defined on the positive real axis such that g(x)= ₀^x t f( t ) dt . If g (x^3 )=x^6+x^7 , then value of _ r=1 ¹⁵ f ( r ^3 ) is :

JEE Main 2025 Solution View → 47

Let f : R R be a twice differentiable function such that f(2)=1 . If F (x)=x f(x) for all x R , ₀^2 x ~F ^ (x) d x=6 and ₀^2 x^2 ~F ^ (x) d x=40 , then F ^ (2)+ ₀^2 ~F (x) d x is e

JEE Main 2025 Solution View → 48

Let for some function y =f(x), ₀^x t f(t) d t=x^2 f(x), x 0 and f(2)=3 . Then f(6) is equal to

JEE Main 2025 Solution View → 49

If _ - 2 ^ 2 96 x^2 ^2 x (1+e^x ) d x= ( ^2+ ), , Z , then ( + )^2 equals

JEE Main 2025 Solution View → 50

IfI (m, n)= ₀^1 x^ m-1 (1-x)^ n-1 d x, m, n 0 , then I(9,14)+I(10,13) is

JEE Main 2025 Solution View → 51

If I = ₀^ 2 ^ 3 2 x ^ 3 2 x+ ^ 3 2 x ~d x , then ₀²¹ x x x ^4 x+ ^4 x ~d x equals :

JEE Main 2025 Solution View → 52

The value of _ e^2 ^ e^4 1 x ( e^ ( ( _e x )^2+1 )⁻¹ e^ ( ( _e x )^2+1 )⁻¹ +e^ ( (6- _e x )^2+1 )⁻¹ ) d x is

JEE Main 2025 Solution View → 53

Let f(x)= ₀^ x^2 t ^2-8 t +15 e ^ t dt , x R . Then the numbers of local maximum and local minimum points of f , respectively, are :

JEE Main 2025 Solution View → 54

Let for f(x)=7 ^8 x+7 ^6 x-3 ^4 x-3 ^2 x, I ₁= ₀^ / 4 f(x) d x and I ₂= ₀^ / 4 x f(x) d x . Then 7 I ₁+12 I ₂ is equal to :

JEE Main 2025 Solution View → 55

Paragraph: Let (f: [0, 2 ] [0,1] ) be the function defined by (f(x)= ^2 x ) and let (g: [0, 2 ] [0, ) ) be the function defined by (g(x)= x 2 -x^2 ). Question: The value of 2 ₀^ 2

JEE Advanced 2024 Solution View → 56

Let (f: [0, 2 ] [0,1] ) be the function defined by (f(x)= ^2 x ) and let (g: [0, 2 ] [0, ) ) be the function defined by (g(x)= x 2 -x^2 ). The value of 16 ^3 ₀^ 2 f(x) g(x) d x is

JEE Advanced 2024 Solution View → 57

Let ₀^x 1- (y^ (t) )^2 d t= ₀^x y(t) d t, 0 x 3, y 0, y(0)=0 . Then at x=2, y^ +y+1 is equal to

JEE Main 2024 Solution View → 58

The value of the integral _ -1 ^2 _e (x+ x^2+1 ) d x is

JEE Main 2024 Solution View → 59

Let _ ^ _e 4 d x e ^x-1 = 6 . Then e ^ and e ^ - are the roots of the equation :

JEE Main 2024 Solution View → 60

The value of k N for which the integral I_n= ₀^1 (1-x^k )^n d x, n N , satisfies 147 I₂₀=148 I₂₁ is

JEE Main 2024 Solution View → 61

Let [t] denote the largest integer less than or equal to t . If ₀^3 ( [x^2 ]+ [ x^2 2 ] ) d x= a + b 2 - 3 - 5 + c 6 - 7 , where a , b , c Z , then a + b + c is equal to_______

JEE Main 2024 Solution View → 62

₀^ / 4 ^2 x ^2 x ( ^3 x+ ^3 x )^2 d x is equal to

JEE Main 2024 Solution View → 63

Let r_k= ₀^1 (1-x^7 )^k d x ₀^1 (1-x^7 )^ k+1 d x , k N . Then the value of _ k=1 ¹⁰ 1 7 (r_k-1 ) is equal to________

JEE Main 2024 Solution View → 64

Let ( m , n )= ₀^1 x^ m -1 (1-x)^ n -1 ~d x, ~m , n >0 . If ₀^1 (1-x¹⁰ )²⁰ ~d x= a ( b , c ) , then 100( a + b + c ) equals____

JEE Main 2024 Solution View → 65

If f(t)= ₀^ 2 x ~d x 1- ^2 t ^2 x , 0 < t < , then the value of ₀^ 2 ^2 dt f( t ) equals_________

JEE Main 2024 Solution View → 66

The value of _ - ^ 2 y(1+ y) 1+ ^2 y d y is :

JEE Main 2024 Solution View → 67

The integral ₀^ / 4 136 x 3 x+5 x d x is equal to :

JEE Main 2024 Solution View → 68

If the value of the integral _ -1 ^1 x 1+3^x d x is 2 . Then, a value of is

JEE Main 2024 Solution View → 69

Let f(x)= array lr -2, & -2 x 0 x-2, & 0 < x 2 array . and h(x)=f(|x|)+|f(x)| . Then _ -2 ^2 h(x) d x is equal to :

JEE Main 2024 Solution View → 70

If ₀^ 4 ^2 x 1+ x x ~d x= 1 a _ e ( a 3 )+ b 3 , where a , b N , then a + b is equal to_________

JEE Main 2024 Solution View → 71

The value of ∫ 0 1 2 x 3 − 3 x 2 − x + 1 1 3 d x is equal to:

JEE Main 2024 Solution View → 72

If ∫ 0 π 3 cos 4 x d x = a π + b 3 , where a and b are rational numbers, then 9 a + 8 b is equal to:

JEE Main 2024 Solution View → 73

Let f : 0 , ∞ → R and F x = ∫ 0 x t f t d t . If F x 2 = x 4 + x 5 , then ∑ r = 1 12 f r 2 is equal to:

JEE Main 2024 Solution View → 74

The value of the integral ∫ 0 π 4 x d x sin 4 2 x + cos 4 2 x equals:

JEE Main 2024 Solution View → 75

If ∫ − π / 2 π / 2 8 2 cos x d x 1 + e sin x 1 + sin 4 x = α π + β log e 3 + 2 2 , where α , β are integers, then α 2 + β 2 equals __________

JEE Main 2024 Solution View → 76

Let f , g : 0 , ∞ → R be two functions defined by f x = ∫ − x x t − t 2 e − t 2 d t and g x = ∫ 0 x 2 t 1 2 e − t 2 d t . Then the value of 9 f log e 9 + g log e 9 is equal to

JEE Main 2024 Solution View → 77

120 π 3 ∫ 0 π x 2 sin x cos x sin 4 x + cos 4 x d x is equal to ______.

JEE Main 2024 Solution View → 78

Let f : ℝ → ℝ be a function defined by f x = 4 x 4 x + 2 and M = ∫ f a f 1 − a x sin 4 x 1 − x d x , N = ∫ f a f 1 − a sin 4 x 1 − x d x ; a ≠ 1 2 . If α M = β N , α , β ∈ ℕ , then

JEE Main 2024 Solution View → 79

Let S = − 1 , ∞ and f : S → ℝ be defined as f x = ∫ − 1 x e t − 1 11 2 t − 1 5 t − 2 7 t − 3 12 2 t − 10 61 d t . Let p = Sum of square of the values of x , where f x attains local

JEE Main 2024 Solution View → 80

If the integral 525 ∫ 0 π 2 sin 2 x cos 11 2 x 1 + cos 5 2 x 1 2 d x is equal to n 2 − 64 , then n is equal to ________

JEE Main 2024 Solution View → 81

Let y = f ( x ) be a thrice differentiable function in ( - 5 , 5 ) . Let the tangents to the curve y = f ( x ) at ( 1 , f ( 1 ) ) and ( 3 , f ( 3 ) ) make angles π 6 and π 4 , resp

JEE Main 2024 Solution View → 82

Let f : R → R be defined f x = a e 2 x + b e x + c x . If f ( 0 ) = - 1 , f ' log e 2 = 21 and ∫ 0 log 4 f x - c x d x = 39 2 , then the value of | a + b + c | equals:

JEE Main 2024 Solution View → 83

The value 9 ∫ 0 9 10 x x + 1 dx , where t denotes the greatest integer less than or equal to t , is _____.

JEE Main 2024 Solution View → 84

The value of lim n → ∞ ∑ k = 1 n n 3 n 2 + k 2 n 2 + 3 k 2 is :

JEE Main 2024 Solution View → 85

If ∫ π 6 π 3 1 - sin 2 x d x = α + β 2 + γ 3 , where α , β and γ are rational numbers, then 3 α + 4 β - γ is equal to _____.

JEE Main 2024 Solution View → 86

If the value of the integral ∫ - π 2 π 2 x 2 cos x 1 + π x + 1 + sin 2 x 1 + e sin x 2023 d x = π 4 π + a - 2 , then the value of a is

JEE Main 2024 Solution View → 87

For x ∈ - π 2 , π 2 , if y x = ∫ cosec x + sin x cosec x sec x + tan x sin 2 x d x and lim x → π 2 - y x = 0 then y π 4 is equal to

JEE Main 2024 Solution View → 88

For 0 < a < 1 , the value of the integral ∫ 0 π d x 1 - 2 a cos x + a 2 is :

JEE Main 2024 Solution View → 89

Let f x = ∫ 0 x g t log e 1 - t 1 + t dt , where g is a continuous odd function. If ∫ - π 2 π 2 f x + x 2 cosx 1 + e x dx = π α 2 - α , then α is equal to _____.

JEE Main 2024 Solution View → 90

If ∫ 0 1 1 3 + x + 1 + x d x = a + b 2 + c 3 , where a , b , c are rational numbers, then 2 a + 3 b - 4 c is equal to :

JEE Main 2024 Solution View → 91

If ( a , b ) be the orthocentre of the triangle whose vertices are ( 1 , 2 ) , ( 2 , 3 ) and ( 3 , 1 ) , and I 1 = ∫ a b xsin 4 x - x 2 dx , I 2 = ∫ a b sin 4 x - x 2 dx , then 36

JEE Main 2024 Solution View → 92

For x &#8712; &#8477; , let tan - 1 x &#8712; - &#960; 2 , &#960; 2 . Then the minimum value of the function f : &#8477; &#8594; &#8477; defined by f x = &#8747; 0 x tan - 1 x e t

JEE Advanced 2023 Solution View → 93

If &#8747; 0 1 1 5 + 2 x - 2 x 2 1 + e 2 - 4 x d x = 1 &#945; log e &#945; + 1 &#946; , &#945; , &#946; &#62; 0 , then &#945; 4 - &#946; 4 is equal to

JEE Main 2023 Solution View → 94

The value of e - &#960; 4 + &#8747; 0 &#960; 4 e - x tan 50 x d x &#8747; 0 &#960; 4 e - x ( tan 49 x + tan 51 x ) d x

JEE Main 2023 Solution View → 95

Let f n = &#8747; 0 &#960; 2 &#8721; k = 1 n sin k - 1 x &#8721; k = 1 n ( 2 k - 1 ) sin k - 1 x cos x d x , n &#8712; &#8469; . Then f 21 - f 20 is equal to

JEE Main 2023 Solution View → 96

Among S 1 : lim n &#8594; &#8734; 1 n 2 ( 2 + 4 + 6 + &#8230; + 2 n ) = 1 S 2 : lim n &#8594; &#8734; 1 n 16 1 15 + 2 15 + 3 15 + &#8230; + n 15 = 1 16

JEE Main 2023 Solution View → 97

Let for x &#8712; &#8477; , S 0 x = x , S k x = C k x + k &#8747; 0 x S k - 1 t d t where C 0 = 1 , C k = 1 - &#8747; 0 1 S k - 1 x d x , k = 1 , 2 , 3 , &#8230; Then S 2 3 + 6 C 3

JEE Main 2023 Solution View → 98

If &#8747; - 0 . 15 0 . 15 100 x 2 - 1 d x = k 3000 , then k is equal to _____.

JEE Main 2023 Solution View → 99

Let the function f : 0 , 2 &#8594; &#8477; be defined as f x = e min x 2 , x - x , x &#8712; [ 0 , 1 ) e x - log e x , x &#8712; 1 , 2 , where t denotes the greatest integer less t

JEE Main 2023 Solution View → 100

If f : &#8477; &#8594; &#8477; be a continuous function satisfying &#8747; 0 &#960; 2 f sin 2 x sin x d x + &#945; &#8747; 0 &#960; 4 f cos 2 x cos x d x = 0 , then the value of &#

JEE Main 2023 Solution View → 101

The value of the integral &#8747; - log e 2 log e 2 e x log e e x + 1 + e 2 x d x is equal to

JEE Main 2023 Solution View → 102

For m , n &#62; 0 , let &#945; m , n = &#8747; 0 2 t m 1 + 3 t n d t . If , 11 &#945; 10 , 6 + 18 &#945; 11 , 5 = p 14 6 , then p is equal to

JEE Main 2023 Solution View → 103

Let f be a continuous function satisfying &#8747; 0 t 2 f ( x ) + x 2 dx = 4 3 t 3 , &#8704; t &#62; 0 . Then f &#960; 2 4 is equal to

JEE Main 2023 Solution View → 104

Let [ t ] denote the greatest integer function. If &#8747; 0 2 . 4 x 2 d x = &#945; + &#946; 2 + &#947; 3 + &#948; 5 , then &#945; + &#946; + &#947; + &#948; is equal to

JEE Main 2023 Solution View → 105

Let [ t ] denote the greatest integer &#8804; t . Then 2 &#960; &#8747; &#960; 6 5 &#960; 6 8 cosec x - 5 cot x d x is equal to _ _ _ _ _ _ _

JEE Main 2023 Solution View → 106

Let f x be a function satisfying f x + f &#960; - x = &#960; 2 , &#8704; x &#8712; &#8477; . Then &#8747; 0 &#960; f x sin x d x is equal to

JEE Main 2023 Solution View → 107

Let f x = x 1 + x n 1 n , x &#8712; &#8477; - - 1 , n &#8712; &#8469; , n &#62; 2 . If f n x = ( f o f o f . . . . upto n times) x , then lim n &#8594; &#8734; &#8747; 0 1 x n - 2

JEE Main 2023 Solution View → 108

The value of the integral &#8747; - &#960; 4 &#960; 4 x + &#960; 4 2 - cos 2 x d x is :

JEE Main 2023 Solution View → 109

If &#8747; 0 &#960; 5 cos x 1 + cos x cos 3 x + cos 2 x + cos 3 x cos 3 x d x 1 + 5 cos x = k &#960; 16 , then k is equal to _____ .

JEE Main 2023 Solution View → 110

lim n &#8594; &#8734; 1 1 + n + 1 2 + n + 1 3 + n + &#8230; + 1 2 n is equal to :-

JEE Main 2023 Solution View → 111

If &#8747; 0 1 x 21 + x 14 + x 7 2 x 14 + 3 x 7 + 6 1 / 7 d x = 1 l 11 m / n where l , m , n &#8712; N , m and n are co-prime then l + m + n is equal to _____ .

JEE Main 2023 Solution View → 112

Let &#945; &#62; 0 . If &#8747; 0 &#945; x x + &#945; - x d x = 16 + 20 2 15 then &#945; is equal to :

JEE Main 2023 Solution View → 113

If &#981; ( x ) = 1 x &#8747; &#960; 4 x 4 2 sin t - 3 &#981; &#39; ( t ) d t , x &#62; 0 then &#981; &#39; &#960; 4 is equal to

JEE Main 2023 Solution View → 114

Let &#945; &#8712; 0 , 1 and &#946; = log e 1 - &#945; . Let P n x = x + x 2 2 + x 3 3 + &#8230; . + x n n , x &#8712; 0 , 1 . Then the integral &#8747; 0 &#945; t 50 1 - t d t is

JEE Main 2023 Solution View → 115

The value of &#8747; &#960; 3 &#960; 2 2 + 3 sin x sin x 1 + cos x d x is equal to

JEE Main 2023 Solution View → 116

Let a differentiable function f satisfy f x + &#8747; 3 x f t t d t = x + 1 , x &#8805; 3 . Then 12 f 8 is equal to:

JEE Main 2023 Solution View → 117

lim n &#8594; &#8734; 3 n 4 + 2 + 1 n 2 + 2 + 2 n 2 + &#8230; + 3 - 1 n 2 is equal to

JEE Main 2023 Solution View → 118

If [ t denotes the greatest integer &#8804; 1 , then the value of 3 e - 1 e &#8747; 1 2 x 2 e x + x 3 d x is :

JEE Main 2023 Solution View → 119

lim x &#8594; 0 48 x 4 &#8747; 0 x t 3 t 6 + 1 d t is equal to

JEE Main 2023 Solution View → 120

The value of the integral &#8747; 1 2 t 4 + 1 t 6 + 1 d t is :

JEE Main 2023 Solution View →
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