Consider the functionfx = x - 1 + x

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 Multiple Choice QuestionsMultiple Choice Questions

1.

What is the area of one of the loops between the curve      y = csin(x) and x-axis ?

  • c

  • 2c

  • 3c

  • 4c


2.

Consider the curves

fx = xx - 1 and gx = 3x2, x > 02x,   x  0

What is the area bounded by the curves ?

  • 176 square units

  • 83 square units

  • 2 square units

  • 13 square units


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3.

Consider the function

fx = x - 1 + x2

where, x  

What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 12 and x = 1 ?

  • 512 square unit

  • 56 square unit

  • 76 square unit

  • 2 square unit


A.

512 square unit

fx = x - 1 + x2fx = x2 +x - 1, for x  1x2 - x + 1, for x < 1

Required area = 

A = 121x2 - x + 1dx = x33 - x22 + x121    = 1 - 183 - 1 - 142 + 1 - 12 = 512 square unit


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4.

Consider the curves

y = x - 1 and x = 2

What is/are the point(s) of intersection of the curves ?

  • ( - 2, 3) only

  • (2, 1) only

  • ( - 2, 3) and (2, 1)

  • Neither ( - 2, 3) nor (2, 1)


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5.

Consider the curves

y = x - 1 and x = 2

What is the area of the region bounded by the curves and x-axis ?

  • 3 square unit

  • 4 square unit

  • 5 square unit

  • 6 square unit


6.

What is the arebounded by thcurvey = 1 - x2 ?

  • 43 square units

  • 83 square units

  • 4 square units

  • 163 square units


7.

What is the area of the region boundedby |x| < 5, y = 0 and y = 8 ?

  • 40 square units

  • 80 square units

  • 120 square units

  • 160 square units


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