Integrals MCQs Type Questions with Answer for ISC Class 12

MCQs Integrals for ISC Class 12 Questions with Answers

Question 1: ₀∫^π sin² x dx =

(a) π/2

(b) π/4

(c) 2π

(d) 4π

Answer: (a) π/2

 

Question 2: ∫dxsin2xcos2x equals

(a) tan x + cot x + c
(b) tan x – cot x + c
(c) tan x cot x + c
(d) tan x – cot 2x + c.

Answer: (b) tan x – cot x + c

Question 3:  ₁∫² dx/x² equals

(a) 1

(b) -1

(c) 2

(d) ½

Answer: (d) ½

Question 4: ∫e^x sec x (1 + tan x) dx equals

(a) e^x cos x + c
(b) e^x sec x + c
(c) e^x sin x + c
(d) e^x tan x + c

Answer: (b) e^x sec x + c

Question 5: If f(x) = ∫x⁰ t sin t dt, then f'(x) is

(a) cos x + x sin x
(b) x sin x
(c) x cos x
(d) sin x + x cos x

Answer: (b) x sin x

Question 6:  ₀∫^π sin² x dx =

(a) π/2

(b) π/4

(c) 2π

(d) 4π

Answer: (a) π/2

Question 7: ₀∫⁴ 3x dx equals

(a) 12

(b) 24

(c) 48

(d) 86

Answer: (b) 24

Question 8: 

(a) 2(sin x + x cos θ) + C
(b) 2(sin x – x cos θ) + C
(c) 2(sin x + 2x cos θ) + C
(d) 2(sin x – 2x cos θ) + C

Answer: (a) 2(sin x + x cos θ) + C

Question 9:  Integrate ₀∫² (x²+x+1) dx

(a) 15/2

(b) 20/5

(c) 20/3

(d) 3/20

Answer: (c) 20/3

Question 10: 

Answer: (a)

Question 11: Find the integral of 8x³+1.

(a) 2x⁴+x+C
(b) 2x⁶-5x+C
(c) 2x⁴-x+C
(d) 2x⁴+x² C

Answer: (a) 2x⁴+x+C

Question 12: Given ∫ 2^x dx = f(x) + C, then f(x) is

Answer: (c)

Question 12: 

(a) sin² x – cos² x + C
(b) -1
(c) tan x + cot x + C
(d) tan x – cot x + C

Answer: (d) tan x – cot x + C

Question 13: 

(a) log |sin x + cos x|
(b) x
(c) log |x|
(d) -x

Answer: (d) -x

Question 14:  ∫cot²x dx equals to

(a) cot x – x + C
(b) cot x + x + C
(c) -cot x + x + C
(d) -cot x – x + C

Answer: (d) -cot x – x + C

Question 15:  

(a) I₁ > I₂
(b) I₂ > I₁
(c) I₁ = I₂
(d) I₁ > 2I₂

Answer: (b) I₂ > I₁

Question 16: If (d/dx) f(x) is g(x), then the antiderivative of g(x) is

(a) f(x)

(b) f’(x)

(c) g’(x)

(d) None of the above

Answer: (a) f(x)

Question 17:  ∫cot²x dx equals to

(a) cot x – x + C

(b) -cot x – x + C

(c) cot x + x + C

(d) -cot x + x + C

Answer: (b) -cot x – x + C

Question 18:  ₀∫² x² dx =

(a) 2

(b) ⅔

(c) 8/3

(d) None of these

Answer: (c) 8/3

Question 19: Let I_n = ∫tan” x dx, (n > 1).
If I₄ + I₆ = a tan⁵ x + bx⁵ + c, where c is a constant of integration, then the ordered pair (a, b) is equal to

(a) (1/5, -1)
(b) (-1/5, 0)
(c) (-1/5, 1)
(d) (1/5, 0)

Answer: (d) (1/5, 0)

Question 20:  Evaluate: ∫(2tan x – 3cot x)² dx

(a) -4tan x – 9cot x – 25x + C
(b) 4tan x – 9cot x – 25x + C
(c) -4tan x + 9 cot x + 25x + C
(d) 4tan x + 9cot x + 25x + C

Answer: (ii) 4tan x – 9cot x – 25x + C

Question 21: ∫ex(1+x)cos2(xe2) dx is equals to

(a) -cot (xe^x) + c
(b) tan (xe^x) + c
(c) tan (e^x) + c
(d) cot (e^x) + c

Answer: (b) tan (xe^x) + c

Question 22: ∫dxx2+2x+2 equals

(a) x tan^-1 (x + 1) + c
(b) tan^-1 (x + 1) + c
(c) (x + 1) tan^-1 x + c
(d) tan^-1 x + c

Answer: (b) tan^-1 (x + 1) + c

Question 23: ∫e^x(cos x – sin x)dx is equal to

(a) e^x – cos x + c
(b) e^x sin x + c
(c) -e^x cos x + c
(d) -e^x sin x + c.

Answer: (a) e^x – cos x + c

Question 24:  If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is

(a) -4

(b) -¼

(c) 3

(d) 7

Answer: (b) -¼

Question 25: ∫tan^-1 √x dx is equal to

(a) (x + 1)tan^-1 √x – √x + c
(b) x tan^-1 √x – √x + c
(c) √x – x tan^-1 √x + c
(d) ^-1x – (x + 1) tan^-1 √x + c

Answer: (a) (x + 1)tan^-1 √x – √x + c

Question 26: ∫b^c |x cos πx|dx is equal to

(a) 8/π

(b) 4/π

(c) 2/π

(d) 1/π

Answer: (a) 8/π

Question 27: ₀∫² (x² + 3)dx equals

(a) 24/3

(b) 25/3

(c) 26/3

(d) None of the above.

Answer: (c) 26/3

Question 28:  If ∫ 2x dx = f(x) + C, then f(x) is

(a) 2^x

(b) 2^x log_e2

(c) 2^x / log_e2

(d) 2^x+1/x+1

Answer: (c) 2^x / log_e2

Question 29: ∫1.dx =

(a) x + k
(b) 1 + k
(c) 𝑥²/2 + k
(d) log x + k

Answer: (a) x + k

Question 30: ∫sin2x–cos2xsin2xcos2x dx is equals to

(a) tan x + cot x + c
(b) tan x + cosec x + c
(c) -tan x + cot x + c
(d) tan x + sec x + c.

Answer: (a) tan x + cot x + c

Question 31: Evaluate: ∫(2 tan x – 3 cot x)² dx

(a) -4tan x – cot x – 25x + C
(b) 4 tan x – 9 cot x – 25x + C
(c) – 4 tan x + 9 cot x + 25x + C
(d) 4 tan x + 9 cot x + 25x + C

Answer: (b) 4 tan x – 9 cot x – 25x + C

Question 32: ∫²_-2 |x|dx =

(a) 0
(b) 2
(c) 1
(d) 4

Answer: (d) 4

Question 33: If a is such that ∫𝑎⁰𝑥𝑑𝑥 ≤ a + 4, then

(a) 0 ≤ a ≤ 4
(b) -2 ≤ a ≤ 0
(c) a ≤ -2 or a ≤ 4
(d) -2 ≤ a ≤ 4

Answer: (d) -2 ≤ a ≤ 4

Question 34: 𝑑/𝑑𝑥∫f(x)dx is equal to

(a) f'(x)
(b) f(x)
(c) f'(x’)
(d) f(x) + c

Answer: (b) f(x)

Question 35: 

∫tan^-1 √xdx is equal to

(a) (x + 1)tan^-1 √x – √x + C
(b) x tan^-1 √x – √x + C
(c) √x – x tan^-1 √x + C
(d) √x – (x + 1)tan^-1 √x + C

Answer: (a) (x + 1)tan^-1 √x – √x + C

–: End of Integrals MCQs Type Questions with Answer for ISC Class 12   :–