The area of the plane region bounded by the curve x = y2 - 2

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 Multiple Choice QuestionsMultiple Choice Questions

61.

The area bounded by the parabola y2 = 8x and its latusrectum (in sq unit) is

  • 16/3

  • 32/3

  • 8/3

  • 64/3


62.

The area bounded by y = sin-1x, x = 12and x - axis is

  • 12 + 1sq unit

  • 1 - 12 sq unit

  • π42 sq unit

  • π42 + 12 - 1 sq unit


63.

The area between the curve y = 1 - x and the x-axis is equal to

  • 1 sq unit

  • 12 sq unit

  • 13

  • 2 sq unit


64.

The value of e-1edtt1 + t is equal to

  • 0

  • loge1 + e

  • log11 + e

  • 1


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65.

The figure shows a triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x is equal to

 

  • 35

  • 34

  • 78

  • 56


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66.

The area of the plane region bounded by the curve x = y- 2 and the· line y = - x is (in square units)

  • 133

  • 25

  • 92

  • 52


C.

92

Given curves x = y2 - 2 and y = x

Thus, interection point are

(- 1, 1) and (2, - 2)

We are to find the area of shaded part

Area of ABC = - 2- 1x + 2dx

    = 23x + 232- 2- 1 = 23 sq unit

Area of BCO = - 10 - xdx = - x22- 10

                     = 12 sq unit

Area of ADO

= - 20x + 2dx = 23x + 232- 20= 432

Area of ODE = area of ODEF - area of OPE

02x + 2dx - 02- xdx= 23x + 23202 - - x2202= 163 - 423 - 2

   [  neglecting the negative sign]

 Required area

23 + 12 + 423 + 163 - 423 - 2

23 + 12 + 163 - 2

276

92 sq unit


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67.

The area bounded by the curve y = sin(x) between x = 0 and x = 2π is (in square units)

  • 1

  • 2

  • 0

  • 4


68.

The area bounded by y = x + 2, y = 2 - x and the x-axis is (in square units)

  • 1

  • 2

  • 4

  • 6


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69.

Area bounded by the curve y = log (x - 2), x-axis and x = 4 is equal to

  • 2log(2) + 1

  • log(2) - 1

  • log(2) + 1

  • 2log(2) - 1


70.

Area bounded by the curves y = ex, y = e- x and the straight line x = 1 is (in sq units)

  • e + 1e

  •  e + 1e + 2

  • e + 1e - 2

  • e - 1e + 2


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