MCQ On Class 12 Maths Chapter 7 Integrals

(1) ∫ |x| dx is equal to

[A] 1/2 x² + C

[B] –x²/2 + C

[C] x|x| + C

[D] 1/2 x|x| + C

Answer: 1/2 x|x| + C

(2) Evaluate:

[A] log|sec x + tan x| – 2 tan(x/2) + C

[B] log|sec x – tan x| – 2 tan(x/2) + C

[C] log|sec x + tan x| + 2 tan(x/2) + C

[D] None of these

Answer: log|sec x + tan x| – 2 tan(x/2) + C

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(3)

[A] a log |tan^-1 x| + C

[B] 1/2(tan^-1 x)² + C

[C] a log (1 + x²) + C

[D] None of these

Answer: a log |tan^-1 x| + C

(4) Evaluate: ∫ sec^4/3 x cosec^8/3 xdx

[A] 3/5 tan^-5/3 x – 3 tan^1/3 x + C

[B] –3/5 tan^-5/3 x + 3 tan^1/3 + C

[C] –3/5 tan^-05/3 x – 3 tan^1/3 + C

[D] inversely proportional to the surface area

Answer: None of these

(5) 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: 4 tan x – 9 cot x – 25x + C

(6)

dx is equal to

[A] 1

[B] 2

[C] 3

[D] 4

Answer: 4

(7)

is equal to

[A]

[B]

[C]

[D]

Answer:

(8) ∫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: (x + 1)tan^-1 √x – √x + C

(9) ∫x² sin x³ dx =

[A] 1/3 cos x³ + c

[B] –1/3 cos x + c

[C] −1/3 cos x³ + c

[D] 1/2 sin² x³ + c

Answer: −1/3 cos x³ + c

(10) dθ =

[A] tan θ – θ + c

[B] θ + tan θ + c

[C] θ – tan θ + c

[D] -θ – cot θ + c

Answer: θ – tan θ + c

(11) dx =

[A] 1 – log 2

[B] 2

[C] 1 + log 2

[D] log 2

Answer: 1 – log 2

(12) What is the value of dx?

[A] 0

[B] π

[C] -π

[D] π/2

Answer: π/2

(13) dx =

[A] log 2

[B] -log 2

[C] log 2 – 1

[D] log 4 – 1

Answer: log 2

(14) What is the value of dx?

[A] 3/2

[B] 1/2

[C] e

[D] 1/e

Answer: 3/2

(15) What is the value of

[A] 1/2 log(-l)

[B] log(- 1)

[C] log 3

[D] log √3

Answer: log 3

(16)

[A] 1

[B] 2

[C] π/4

[D] π²/8

Answer: 2

(17)

[A] -1

[B] 0

[C] 1

[D] None of these

Answer: 0

(18) What is the value of

sin³ x cos² xdx?

[A] 0

[B] 1

[C] 1/2

[D] 2

Answer: 0

(19) dx is equal to

[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: 2 (sin x + x cos θ) + C

(20)

dx =

[A] log(sin x – cos x)

[B] x

[C] log x

[D] log sin (cos x)

Answer: x

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