JEE Main Previous Year Questions (2026): Indefinite Integral

[JEE Main MCQs]

Q1: If  where C is a constant of integration, then  can be:
(a)
(b)
(c)
(d)
Ans: (c)



Q2: If  where c is a constant of integration, then g(0) is equal to:
(a) 1
(b) 2
(c) e
(d) e²
Ans: (b)




Q3: Let  Then f(3) - f(1) is eqaul to:
(a)
(b)
(c)
(d)
Ans: (b)




Q4: The integral  is equal to (where C is a constant of integration):
(a)
(b)
(c)
(d)
Ans: (c)


Q5: If where C is a constant of integration, then the ordered pair (A(x), B(x)) can be:
(a) (x + 1, -√x)
(b) (x + 1, √x)
(c) (x - 1, - √x)
(d) (x - 1, √x)
Ans: (a)

Applying integration by parts,

⇒ x = t² 
⇒ dx = 2tdt


Q6: If  where C is a constant of integration, then the ordered pair (λ, f(θ)) is equal to:
(a) (-1, 1 - tanθ)
(b) (1, 1 + tanθ)
(c) (-1, 1 - tanθ)
(d) (1, 1 - tanθ)
Ans: (c)




Q7: If ƒ'(x) = tan^-1(secx + tanx),  and ƒ(0) = 0, then ƒ(1) is equal to:
(a) 1/4
(b)
(c)
(d)
Ans: (c)
ƒ'(x) = tan^-1(secx + tanx)



Q8: The integral  is equal to: (where C is a constant of integration)
(a)
(b)
(c)
(d)
Ans: (b)



Q9: Ifwhere c is a constant of integration, then λf(π/3) is equal to:
(a) 9/8
(b) 2
(c) -2
(d)
Ans: (c)

Let sin x = t
⇒ cos xdx = dt