MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers

  

Integrals Class 12 MCQs Questions with Answers

Question 1.
∫x+sinx1+cosx dx is equal to
(a) log |1 + cos x | + c
(b) log | x + sin x | + c
(c) x – tan + c
(d) x. tan x2 + c

Answer

Answer: (d) x. tan x2 + c

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Question 2.
∫1.dx =
(a) x + k
(b) 1 + k
(c) x22 + k
(d) log x + k

Answer

Answer: (a) x + k

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Question 3.
∫dx√x =
(a) √x + k
(b) 2√x + k
(c) x + k
(d) 23x3/2 + k

Answer

Answer: (b) 2√x + k

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Question 4.
∫dx1+cosx =
(a) tan x2 + k
(b) 12 tan x2 + k
(c) 2 tan x2 + k
(d) tan² x2 + k

Answer

Answer: (a) tan x2 + k

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Question 5.
∫ba x5 dx =
(a) tan x2 + k
(b) 12 tan x2 + k
(c) 2 tan x2 + k
(d) tan² x2 + k

Answer

Answer: (a) tan x2 + k

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Question 6.
If x > a, ∫dxx2−a2 =
(a) 22a log x−ax+a + k
(b) 22a log x+ax−a + k
(c) 1a log(x² – a²) + k
(d) log(x + x2−a2−−−−−−√ + k)

Answer

Answer: (a) 22a log x−ax+a + k

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Question 7.
∫cos2xdx(sinx+cosx)2 =
(a) –1sinx+cosx + c
(b) log | sin x + cos x | + c
(c) log | sin x – cos x | + c
(d) 1(sinx+cosx)2

Answer

Answer: (b) log | sin x + cos x | + c

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Question 8.
∫(1+logx)21+x2 dx =
(a) 13(1+log)³ + c
(b) 12(1+log)² + c
(c) log (log 1 + x) + 2
(d) None of these

Answer

Answer: (a) 13(1+log)³ + c

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Question 9.
∫10(tan−1x)21+x2 dx =
(a) 1
(b) π264
(c) π2192
(d) None of these

Answer

Answer: (c) π2192

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Question 10.
∫2−2 |x|dx =
(a) 0
(b) 2
(c) 1
(d) 4

Answer

Answer: (d) 4

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Question 11.
∫x4+1x2+1 dx is equal to
(a) x33 + x + tan-1 x + c
(b) x33 – x + tan x + c
(c) x33 + x + 2tan-1 x + c
(d) x33 – x + 2tan-1 x + c

Answer

Answer: (d) x33 – x + 2tan-1 x + c

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Question 12.
∫(√x + 1√x) dx =
(a) 1x x13 + 2x12 + c
(b) 23 x23 + 12x2 + c
(c) 23 x32 + 2x12 + c
(d) 32 x32 + 12x12 + c

Answer

Answer: (c) 23 x32 + 2x12 + c

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Question 13.
∫sin2x−cos2xsin2xcos2x dx is equal to
(a) tan x + cos x + c
(b) tan x + cosec x + c
(c) tan x + cot x + c
(d) tan x+ sec x + c

Answer

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

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Question 14.
ddx∫f(x)dx is equal to
(a) f'(x)
(b) f(x)
(c) f'(x’)
(d) f(x) + c

Answer

Answer: (b) f(x)

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Question 15.
∫xdx(x−1)(x−2) equals

(d) log |(x – 1)(x – 2) + c

Answer

Answer: (b) log|(x−2)2x−2| + c

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Question 16.
What is the value of ∫π/20 tanx√tanx√+cotx√ dx?
(a) π2
(b) π4
(c) π8
(d) None of these

Answer

Answer: (b) π4

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Question 17.
What is the value of ∫π/20 sinx–cosx1+sinxcosx dx?
(a) 1
(b) π2
(c) 0
(d) –π2

Answer

Answer: (c) 0

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Question 18.
What is the value of ∫π/3π/6 dxsin2x?
(a) 12 log(-l)
(b) log(- 1)
(c) log 3
(d) log √3

Answer

Answer: (c) log 3

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Question 19.
What is the value of ∫1−1 sin³ x cos² xdx?
(a) 0
(b) 1
(c) 12
(d) 2

Answer

Answer: (a) 0

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Question 20.
What is the value of ∫e11+logxx dx?
(a) 32
(b) 12
(c) e
(d) 1e

Answer

Answer: (a) 32

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Question 21.
∫π/2−π/2 sin9 xdx =
(a) -1
(b) 0
(c) 1
(d) None of these

Answer

Answer: (b) 0

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Question 22.
∫π2/40siny√y√
(a) 1
(b) 2
(c) π4
(d) π28

Answer

Answer: (b) 2

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Question 23.
∫∞011+ex dx =
(a) log 2
(b) -log 2
(c) log 2 – 1
(d) log 4 – 1

Answer

Answer: (a) log 2

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Question 24.
∫10 x(1 – x)99 is equal to
(a) 110010
(b) 110100
(c) 11010
(d) 1110100

Answer

Answer: (b) 110100

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Question 25.
What is the value of ∫10 ddx{sin-1(2x1+x2)}dx?
(a) 0
(b) π
(c) -π
(d) π2

Answer

Answer: (d) π2

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Question 26.
∫10 x1+x dx =
(a) 1 – log 2
(b) 2
(c) 1 + log 2
(d) log 2

Answer

Answer: (a) 1 – log 2

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Question 27.
∫sinx+cosx1+2sinx√ dx =
(a) log(sin x – cos x)
(b) x
(c) log x
(d) log sin (cos x)

Answer

Answer: (b) x

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Question 28.
∫log10 xdx =
(a) loge 10.x loge (xe) + c
(b) log10 e.x loge (xe) + c
(c) (x – 1) loge x + c
(d) 1x + c

Answer

Answer: (b) log10 e.x loge (xe) + c

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Question 29.
∫(cos2θ–1cos2θ+1) dθ =
(a) tan θ – θ + c
(b) θ + tan θ + c
(c) θ – tan θ + c
(d) -θ – cot θ + c

Answer

Answer: (c) θ – tan θ + c

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Question 30.
∫2dx1−4x2√ =
(a) tan-1 (2x) + c
(b) cot-1 (2x) + c
(c) cos-1 (2x) + c
(d) sin-1 (2x) + c

Answer

Answer: (d) sin-1 (2x) + c

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Question 31.
Value of ∫dx2x–x2√
(a) sin-1 (x – 1) + c
(b) sin-1 (1 + x) + c
(c) sin-1 (1 + x²) + c
(d) –2x−x2−−−−−−√ + c

Answer

Answer: (a) sin-1 (x – 1) + c

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Question 32.
∫x² sin x³ dx =
(a) 13 cos x³ + c
(b) –13 cos x + c
(c) −13 cos x³ + c
(d) 12 sin² x³ + c

Answer

Answer: (c) −13 cos x³ + c

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Question 33.
∫cos2x−cos2θcosx–cosθdx 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

Answer: (a) 2 (sin x + x cos θ) + C

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Question 34.
∫dxsin(x−a)sin(x−b) is equal to
(a) sin(b – a) log |sin(x−b)sin(x−a)| + C
(b) cosec (b – a) log |sin(x−b)sin(x−b)| + C
(c) cosec (b – a) log |sin(x−b)sin(x−a)| + C
(d) sin (b – a) log |sin(x−a)sin(x−b)| + C

Answer

Answer: (c) cosec (b – a) log |sin(x−b)sin(x−a)| + C

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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

Answer: (a) (x + 1)tan-1 √x – √x + C

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Question 36.
∫ex(1−x1+x2)² dx is equal to
(a) ex1+x2 + C
(b) –−ex1+x2 + C
(c) ex(1+x2)2 + C
(d) −ex(1+x2)2 + C

Answer

Answer: (a) ex1+x2 + C

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Question 37.
∫x9(4x2+1)6 dx is equal to

Answer

Answer: (d) 110 (1x2 + 4)-5 + C

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Question 38.
If ∫dx(x+2)(x2+1) = a log |1 + x²| + b tan-1 x + 15 log |x + 2| + C, then
(a) a = −110, b = −25
(b) a = 110, b = −25
(c) a = −110, b = 25
(d) a = 110, b = 25

Answer

Answer: (c) a = −110, b = 25

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Question 39.
∫ x3x+1 is equal to
(a) x + x22 + x33 – log |1 – x| + C
(b) x + x22 – x33 – log |1 – x| + C
(c) x + x22 – x33 – log |1 + x| + C
(d) x + x22 + x33 – log |1 + x| + C

Answer

Answer: (d) x + x22 + x33 – log |1 + x| + C

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Question 40.
If ∫x3dx1+x2√ = a(1 + x²)3/2 + b1+x2−−−−−√ + C, then
(a) a = 13, b = 1
(b) a = −13, b = 1
(c) a = −13, b = -1
(d) a = 13, b = -1

Answer

13

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Question 41.
∫π/4−π/4 dx1+cos2x dx is equal to
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (a) 1

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Question 42.
∫π/20 1+sin2x−−−−−−−−√ dx is equal to
(a) 2√2
(b) 2(√2 + 1)
(c) 0
(d) 2(√2 – 1)

Answer

Answer: (c) 0

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Question 43.
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

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

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Question 44.
Evaluate: ∫ sec²(7 – 4x)dx
(a) –14 tan(7 – 4x) + C
(b) 14 tan(7 – 4x) + C
(c) 14 tan(7 + 4x) + C
(d) –14 tan(7x – 4) + C

Answer

Answer: (a) –14 tan(7 – 4x) + C

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Question 45.
∫ 10x9+10xloge1010x+x10 dx is equal to
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10)-1 + C
(d) loge(10x + x10) + C

Answer

Answer: (d) loge(10x + x10) + C

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Question 46.
Evaluate: ∫ sec4/3 x cosec8/3 xdx
(a) 35 tan-5/3 x – 3 tan1/3 x + C
(b) –35 tan-5/3 x + 3 tan1/3 + C
(c) –35 tan-05/3 x – 3 tan1/3 + C
(d) None of these

Answer

Answer: (b) –35 tan-5/3 x + 3 tan1/3 + C

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Question 47.
∫ a(1+x2)tan−1x dx =
(a) a log |tan-1 x| + C
(b) 12(tan-1 x)² + C
(c) a log (1 + x2) + C
(d) None of these

Answer

Answer: (a) a log |tan-1 x| + C

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Question 48.
∫ cotxsinx√3 dx =
(a) −3sinx√3 + C
(b) −2sin3x + C
(c) 3sin1/3x + C
(d) None of these

Answer

Answer: (a) −3sinx√3 + C

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Question 49.
Evaluate: ∫ 11+3sin2x+8cos2x dx
(a) 16 tan-1 (2 tan x) + C
(b) tan-1 (2 tan x) + C
(c) 16 tan-1(2tanx3) + C
(d) None of these

Answer

Answer: (c) 16 tan-1(2tanx3) + C

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Question 50.
Evaluate: ∫ 19+8x−x2√ dx
(a) -sin-1 (x−45) + C
(b) sin-1 (x+45) + C
(c) sin-1 (x−45) + C
(d) None of these

Answer

Answer: (c) sin-1 (x−45) + C

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Question 51.
∫ dx1−cosx−sinx is equal to
(a) log |1 + cotx2| + C
(b) log |1 – tanx2| + C
(c) log |1 – cotx2| + C
(d) log |1 + tanx2| + C

Answer

Answer: (c) log |1 – cotx2| + C

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Question 52.
Evaluate: ∫ 11−e2x√ dx
(a) log |e-x + e−2x–1−−−−−−√| + C
(b) -log |e-x + e−2x–1−−−−−−√| + C
(c) -log |e-x – e−2x–1−−−−−−√| + C
(d) None of these

Answer

Answer: (b) -log |e-x + Missing close brace| + C

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Question 53.
If ∫ 3x+4x3−2x−4 dx = log |x – 2| + k log f(x) + c, then
(a) f(x) = |x² + 2x + 2|
(b) f(x) = x² + 2x + 2
(c) k = –12
(d) All of these

Answer

Answer: (d) All of these

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Question 54.
Evaluate: ∫ 1−cosxcosx(1+cosx) dx
(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

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

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Question 55.
∫ cos(loge.x)dx is equal to
(a) 12 x[cos (logex) + sin(logex)]
(b) x[cos (logex) + sin(logex)]
(c) 12 x[cos (logex) – sin(logex)]
(d) x[cos (logex) – sin(logex)]

Answer

Answer: (b) –35 tan-5/3 x + 3 tan1/3 + C

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Question 56.
∫ |x| dx is equal to
(a) 12 x² + C
(b) –x22 + C
(c) x|x| + C
(d) 12 x|x| + C

Answer

Answer: (d) 12 x|x| + C

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Question 57.
∫ sin-1 xdx is equal to
(a) cos-1 x + C
(b) x sin-1x + 1−x2−−−−−√ + C
(c) 11−x2√ + C
(d) x sin-1x – 1−x2−−−−−√ + C

Answer

Answer: (b) x sin-1x + 1−x2−−−−−√ + C

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Question 58.
∫ cos-1(1x)dx equals
(a) x sec-1 x + log |x + x2−1−−−−−√| + C
(b) x sec-1 x – log |x + x2−1−−−−−√| + C
(c) -x sec-1 x – log |x + x2−1−−−−−√| + C
(d) None of these

Answer

Answer: (b) x sec-1 x – log |x + x2−1−−−−−√| + C

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