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Integrals

JEE Main 2024 (Online) 9th April Evening ShiftMCQMedium📈 Topic in 17% papers+4−1
Ques. 1JEE Main 2024, 9 April (Evening Shift)

The value of the integral -12 e (x + x2 + 1 ) dx is

  1. 5 - 2 + e ( 7 + 4 51 + 2 )
  2. 2 - 5 + e ( 7 + 4 51 + 2 )
  3. 5 - 2 + e ( 9 + 4 51 + 2 )
  4. 2 - 5 + e ( 9 + 4 51 + 2 )

Answer

(4) 2 - 5 + e ( 9 + 4 51 + 2 )

Solution

Integrating by parts (first function e(x + x2 + 1), whose derivative is 1 x2 + 1):

e (x + x2 + 1 ) dx = x e (x + x2 + 1 ) - x2 + 1

At x = 2: 2 e(2 + 5) - 5; at x = -1: - e( 2 - 1) - 2 = e( 2 + 1) - 2

I = 2 e(2 + 5) - e(1 + 2) - 5 + 2

Since (2 + 5)2 = 9 + 4 5,

I = 2 - 5 + e ( 9 + 4 51 + 2 )

Answer: (4)

Keep practising — Integrals

Ques. 2JEE Main 2024, 8 April (Morning Shift)

The value of k N for which the integral In = 01 (1 - xk )n dx, n N, satisfies 147 I20 = 148 I21 is

  1. 8
  2. 14
  3. 7
  4. 10
Ques. 3JEE Main 2024, 8 April (Morning Shift)

Let I(x) = 6 2 x(1 - x)2 dx. If I(0) = 3, then I ( 12 ) is equal to

  1. 3
  2. 2 3
  3. 6 3
  4. 3 3
Ques. 4JEE Main 2024, 8 April (Evening Shift)

Let e 4 dx ex - 1 = 6. Then e and e- are the roots of the equation :

  1. 2x2 - 5x + 2 = 0
  2. x2 - 2x - 8 = 0
  3. 2x2 - 5x - 2 = 0
  4. x2 + 2x - 8 = 0
Ques. 5JEE Main 2024, 8 April (Evening Shift)

If 1 [5](x - 1)4(x + 3)6 dx = A ( x - 1 x + 3 )B + C, where C is the constant of integration, then the value of + + 20AB is .

Ques. 6JEE Main 2024, 6 April (Morning Shift)

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

  1. 1/9
  2. 1/6
  3. 1/3
  4. 1/12
Ques. 7JEE Main 2024, 6 April (Morning Shift)

Let rk = 01 (1 - x7 )k dx 01 (1 - x7 )k+1 dx, k N. Then the value of k=110 17 (rk - 1 ) is equal to .

Ques. 8JEE Main 2024, 6 April (Evening Shift)

If 1a2 2 x + b2 2 x dx = 112 -1(3 x) + constant, then the maximum value of a x + b x, is :

  1. 41
  2. 39
  3. 40
  4. 42
Ques. 9JEE Main 2024, 6 April (Evening Shift)

Let [t] denote the largest integer less than or equal to t. If 03 ( [x2 ] + [ x22 ] )dx = a + b 2 - 3 - 5 + c 6 - 7, where a, b, c Z, then a + b + c is equal to .

Ques. 10JEE Main 2024, 5 April (Morning Shift)

The integral 0 /4 136 x3 x + 5 x dx is equal to :

  1. 3 - 50 e 2 + 20 e 5
  2. 3 - 25 e 2 + 10 e 5
  3. 3 - 10 e(2 2) + 10 e 5
  4. 3 - 30 e 2 + 20 e 5
Ques. 11JEE Main 2024, 5 April (Morning Shift)

The value of - 2y(1 + y)1 + 2 y dy is :

  1. 2
  2. 2
  3. 22
  4. 2 2

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