The value of ∫e-1edtt1 + t is equal to f

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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


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64.

The value of e-1edtt1 + t is equal to

  • 0

  • loge1 + e

  • log11 + e

  • 1


D.

1

Let I = e- 1edttt + 1= e- 1e1tdt - e- 1e1t + 1dt= logt - logt + 1e- 1e= loge - loge + 1 - loge- 1 - loge- 1 + 1= logee +1 - - loge - loge- 1 + 1=  logee +1 + loge1e + 1= logee = 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


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


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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