JEE Main Previous year questions (2021-2026): Indefinite Integrals

Q.1. For then
(a)

(b)

(c)

(d)

Ans. a

Given,

Given,

From option (A),

Q.2. The integralis equal to 

(a)

(b)
(c)

(d)

Ans. a

Q.3. If is equal to :

(a)

(b)

(c)

(d)

Ans. a

Q.4. Ifwhere C is a constant, thenat x = 1 is equal to :

(a)

(b) 3/4
(c)

(d) 3/2

Ans. b

for x = 1

Q.5. The integral is equal to : (where C is a constant of integration)

(a)

(b)

(c)

(d)

Ans. c

Q.6. The integralis equal to (where c is a constant of integration)

(a)

(b)

(c)

(d)

Ans. a

(2x - 1)² + 5 = t²
(2(2x - 1) 2dx = 2t dt

Q.7. The integralx > 0, is equal to : (where c is a constant of integration)

(a)

(b)

(c)

(d)

Ans. c


Here c is integral constant.

Q.8. The value of the integral

(a)

(b)

(c)

(d)

Ans. c

Let sinθ = t, cos θdθ = dt

Let 2t⁶ + 3t⁴ + 6t² = z
12(t⁵ + t³ + t)dt = dz

Q.9. If  , where c is a constant of integration, then the ordered pair (a, b) is equal to :
(a) (-1,3)
(b) (1,3)
(c) (1,-3)
(d) (3, 1)

Ans. b

Write sin2x = 1 + sin2x - 1

put sin x + cos x = t
⇒(cos x - sin x) dx = dt

∴ a = 1 and b = 3

Q.10. If

when C is constant of integration, then the value of 18(α + β + y²)  is

Ans. 3

Let tan x = t ⇒ sec²x. dx = dt


⇒ A(t² - t + 1) + B(2t - 1)(t² - t + 1) + C(t +1)= t
⇒ t2(A + 2B) + t(-A + B + C) + A - B + C = 1
∴ A + 2B = 0.....(1)
- A + B + C = 1 ...(2)
A - B + C = 0 ....(3)

A + 2B = 0
A - B =

Q.11. If where C is a constant of integration, then u + v is equal to _____________.
∫(2e^x+3e^-x)/(4e^x+7e^-x)dx = 1/14 ux + v log_e(4e^x + 7e^-x))+ C

Ans. 7
∫(2e^x+3e^-x)/(4e^x+7e^-x)dx = 1/14 ux + v log_e(4e^x + 7e^-x))+ C

Aliter :

Q.12. If+ C, x > 0 where C is the constant of integration, then the value of 9 (√3a + b) is equal to _____________.

Ans. 15

Hence,

Q.13. If then the value of K is

Ans. 4

f(0) = 0 ⇒ C = 0

⇒ k = 4

Q.14. For real numbers α, β, γ  and δ , if

where C is an arbitrary constant, then the value of 10(α, βγ + δ) is equal to _____________

Ans. 6

Now

I = I₁ + I₂ =




= 1 + 5 = 6