12th Standard cbse -- Maths - Integrals

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Question - 1

Given ∫ 2x dx = f(x) + C, then f(x) is

  • A 2x
  • B 2x loge2
  • C \(\frac { { 2 }^{ x } }{ { log }_{ e }2 } \)
  • D \(\frac { { 2 }^{ x } }{ { log }_{ e }2 } \)

Question - 2

\(\int { \frac { 1 }{ { sin }^{ 2 }x{ cos }^{ 2 }x } dx } \) is equal to

  • A sin² x – cos² x + C
  • B -1
  • C tan x + cot x + C
  • D tan x – cot x + C

Question - 3

\(\int { \frac { cos2x-cos2\theta }{ cosx-cos\theta } } dx\) 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

Question - 4

 ∫cot²x dx equals to

  • A cot x – x + C
  • B cot x + x + C
  • C -cot x + x + C
  • D -cot x – x + C

Question - 5

\(\int { \frac { sinx+cosx }{ \sqrt { 1+sin2x } } dx, } \)\(\frac { 3\pi }{ 4 } <x<\frac { 7\pi }{ 4 } \) is equal to

  • A log |sin x + cos x|
  • B x
  • C log |x|
  • D -x

Question - 6

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

  • A 7
  • B -4
  • C 3
  • D \(-\frac { 1 }{ 4 } \)

Question - 7

The value of X for which
\(\int { \frac { { 4x }^{ 3 }+\lambda { 4 }^{ x } }{ { 4 }^{ x }+x^{ 4 } } dx } \)\(=log|{ 4 }^{ x }+{ x }^{ 4 }|\)

  • A 1
  • B loge4
  • C loe4 e
  • D 4

Question - 8

If \(\int { \frac { 1 }{ \sqrt { 4-{ 9x }^{ 2 } } } dx } =\frac { 1 }{ 3 } { sin }^{ -1 }(ax)+C\), then value of a is

  • A 2
  • B 4
  • C \(\frac32\)
  • D \(\frac23\)

Question - 9

If x = \(\int _{ 0 }^{ y }{ \frac { dt }{ \sqrt { 1+9{ t }^{ 2 } } } } \) and \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \) = ay then value of a is equal to

  • A 3
  • B 6
  • C 9
  • D 1

Question - 10

\(\int { { e }^{ x }{ \left( \frac { 1-x }{ 1+{ x }^{ 2 } } \right) }^{ 2 } } dx\) is equal to

  • A \(\frac { { e }^{ x } }{ 1+{ x }^{ 2 } } +C\)
  • B \(-\frac { { e }^{ x } }{ 1+{ x }^{ 2 } } +C\)
  • C \(\frac { { e }^{ x } }{ (1+{ x }^{ 2 })^{ 2 } } +C\)
  • D \(\frac { { e }^{ x } }{ (1+{ x }^{ 2 })^{ 2 } } +C\)
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