12th Standard cbse -- Maths - Application of Integrals

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Question - 1

Area bounded by the curve y = sin x and the x-axis between x = 0 and x = 2π is

  • A 2 sq units
  • B 0 sq units
  • C 3 sq units
  • D 4 sq units

Question - 2

Area of the region bounded by the curve y = \(\sqrt { 49-{ x }^{ 2 } } \) and the x-axis is

  • A \(\frac { 49 }{ 2 } \pi \) sq units
  • B 98π sq units
  • C 49π sq units
  • D 240π sq units

Question - 3

Area of the region bounded by the curve x = 2y + 3, the y-axis and between y = -1 and y = 1 is

  • A 4 sq units 3
  • B \(\frac32\)
  • C 6 sq units
  • D 8 sq units

Question - 4

Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is

  • A π
  • B \(\frac { \pi }{ 2 } \)
  • C \(\frac { \pi }{ 3 } \)
  • D \(\frac { \pi }{ 3 } \)

Question - 5

Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is

  • A 2
  • B \(\frac94\)
  • C \(\frac93\)
  • D \(\frac92\)

Question - 6

Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is

  • A 2 (ㅠ – 2)
  • B ㅠ - 2
  • C 2ㅠ - 1
  • D 2(ㅠ+2)

Question - 7

Area lying between the curves y2 = 4x and y = 2x is

  • A \(\frac23\)
  • B \(\frac13\)
  • C \(\frac14\)
  • D \(\frac34\)

Question - 8

Area bounded by the curve y = x3, the x-axis and the ordinates x = – 2 and x = 1 is

  • A -9
  • B \(\frac{-15}{4}\)
  • C \(\frac{15}{4}\)
  • D \(\frac{17}{4}\)

Question - 9

The area bounded by the curve y = x |x| , x-axis and the ordinates x = – 1 and x = 1 is given by

  • A 0
  • B \(\frac13\)
  • C \(\frac23\)
  • D \(\frac43\)

Question - 10

The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is

  • A \(\frac { 4 }{ 3 } (4\pi -\sqrt { 3 } )\)
  • B \(\frac { 4 }{ 3 } (4\pi +\sqrt { 3 } )\)
  • C \(\frac { 4 }{ 3 } (8\pi -\sqrt { 3 } )\)
  • D \(\frac { 4 }{ 3 } (8\pi +\sqrt { 3 } )\)
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