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Integrals · Question 45

JEE Main 2025 (Online) 2nd April Evening ShiftMCQMedium📈 Topic in 71% papers+4−1
1

Let (a, b) be the point of intersection of the curve x2 = 2y and the straight line y - 2x - 6 = 0 in the second quadrant. Then the integral I = ab 9x21 + 5x dx is equal to :

  1. 27
  2. 18
  3. 24
  4. 21

Answer

(3) 24

Solution

Put y = 2x + 6 in x2 = 2y:

x2 = 4x + 12 x2 - 4x - 12 = 0

(x - 6)(x + 2) = 0 x = 6 or x = -2

Second quadrant ⇒ x = -2, y = 2(-2) + 6 = 2

(a, b) = (-2, 2)

I = -22 9x21 + 5x dx

Using -aa f(x) dx = -aa f(-x) dx:

I = -22 9x21 + 5-x dx = -22 9x2 5x5x + 1 dx

Adding the two forms:

2I = -22 9x2 dx = 2 9 233 = 48

I = 24

Answer: (3)

JEE Main 2025 (Online) 2nd April Evening Shift

Keep practising — Integrals

2

4 01 ( 1 3 + x2 + 1 + x2 )dx - 3 e( 3) is equal to :

  1. 2 - 2 - e(1 + 2)
  2. 2 + 2 + e(1 + 2)
  3. 2 + 2 - e(1 + 2)
  4. 2 - 2 + e(1 + 2)
JEE Main 2025 (Online) 2nd April Evening Shift
3

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

  1. 3 4
  2. 4 3
  3. 6 43
  4. 2 3
JEE Main 2025 (Online) 29th January Morning Shift
4

If - 2 2 96x2 2 x(1 + ex) dx = ( 2 + ), , Z, then ( + )2 equals

  1. 196
  2. 100
  3. 64
  4. 144
JEE Main 2025 (Online) 28th January Morning Shift
5

Let f: R R be a twice differentiable function such that f(2) = 1. If F(x) = x f(x) for all x R, 02 x F'(x) dx = 6 and 02 x2 F''(x) dx = 40, then F'(2) + 02 F(x) dx is equal to:

  1. 13
  2. 11
  3. 9
  4. 15
JEE Main 2025 (Online) 28th January Evening Shift
6

If f(x) = 1x1/4 (1 + x1/4 )dx, f(0) = -6, then f(1) is equal to :

  1. 4 ( e 2 - 2 )
  2. e2 2 + 2
  3. 2 - e2
  4. 4 ( e 2 + 2 )
JEE Main 2025 (Online) 28th January Evening Shift
7

Let f be a real valued continuous function defined on the positive real axis such that g(x) = 0x t f(t) dt. If g (x3 ) = x6 + x7, then value of r=115 f (r3 ) is :

  1. 270
  2. 340
  3. 310
  4. 320
JEE Main 2025 (Online) 28th January Evening Shift

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