The area of the region bounded by the curves y = x2 and x = y2&nb

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 Multiple Choice QuestionsMultiple Choice Questions

31.

The area of the region bounded by the curve y = x3, its tangent at (1, 1) and X-axis, is

  • 112 sq units

  • 16 sq units

  • 217 sq units

  • 215 sq units


32.

Area of the region bounded by y = x and y = - x + 2 is

  • 4 sq units

  • 3 sq units

  • 2 sq units

  • 1 sq units


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33.

The area of the region bounded by the curves y = x2 and x = yis

  • 1/3

  • 1/2

  • 1/4

  • 3


A.

1/3

Given curves are y = x2 and x = y2, which is the form of parabola.

The point of intersection, x = (x2)2

 x = x4 x(1 - x3) = 0 x = 0 and 1 = x3 x = 0 and x = 1

When x = 0, then y = 0

When x = 1, then y = 12 = 1

 The point of intersection is (0, 0) and (1, 1).

 Area of shaded region

= 01y2 - y1dx= 01x - x2dx= x3/23/2 - x3301= 2313/2 - 133 - 0 - 0= 23 - 13= 13 sq units


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34.

If f(x) = x23, x  0. Then, the area of the region enclosed by the curve y = f (x) and the three lines y = x, x = 1and x = 8 is

  • 632

  • 935

  • 1057

  • 12910


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35.

If f(x) = x1x - 1 + 1x + 1x + 1, x> 1. Then,

  • f(x)  1

  • 1 < f(x)  2

  • 2 < f(x)  3

  • f(x) > 3


36.

The area of the region enclosed between parabola y2 = x and the line y = mx is 148. Then, the value of m is

  • - 2

  • - 1

  • 1

  • 2


37.

The area of the region bounded by the curves y = x , y = 1x, x = 2 is

  • 4 - loge2

  • 14 + loge2

  • 3 - loge2

  • 154 - loge2


38.

The area of the region, bounded by the curves y = sin- 1(x) + x(1 - x) and y = sin- 1 (x) - x(1 - x) in the first quadrant, is

  • 1

  • 12

  • 13

  • 14


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39.

The area enclosed between y2 = x and y = x is

  • 23 sq unit

  • 12 unit

  • 13 unit

  • 16


40.

The area bounded by y2 = 4x and x = 4y is

  • 203 sq units

  • 163 sq units

  • 143

  • 103


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