The area bounded by the parabola y2 = x, straight line y = 4 and

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91.

The area bounded by the parabola y2 = x, straight line y = 4 and y-axis is square units is

  • 16/3 sq. unit

  • 64/3 sq. unit

  • 72 sq. unit

  • None of these


B.

64/3 sq. unit

Line y = 4 meets the parabola y2 = x at A

 16 = x and A is (16, 4)

 Required area       = y = 04xdy      = y = 04y2dy      = y3304      = 643 sq. unit


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92.

The area of the region bounded by the curves x2 + y2 = 8 and y2 = 2x is

  • 2π + 13

  • π + 13

  • 2π + 43

  • π + 43


93.

The area of the region bounded by the curves, y2 = 8x and y = x is

  • 643

  • 323

  • 163

  • 83


94.

The area of the region bounded by the curve y = 2x - x2 and X - axis is

  • 23 sq units

  • 43 sq units

  • 53 sq units

  • 83 sq units


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95.

The area of the region bounded by the lines y = 2x + 1, y = 3x + 1and x = 4 is

  • 16 sq unit

  • 1213 sq unit

  • 1216 sq unit

  • 8 sq unit


96.

A closed figure S is bounded by the hyperbola x2 - y2 = a2 and the straight line x = a + h; (h > 0, a > 0). This closed figure is rotated about the X-axis. Then, the volume of the solid ofrevolution is

  • πh23a + h

  • πh263a + h

  • πh233a + h

  • πh223a + h


97.

The centre of gravity (centre of mass) of a rod (of length L), whose linear mass density varies as the square of the distance from one end is at

  • 3L5

  • 2L5

  • L3

  • 3L4


98.

The part of straight line y = x between x = 1 and x = 2 is revolved about X-axis, then the curved surface area of the solid thus generated is

  • 22π

  • 32

  • 32π

  • None of these


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99.

The area of the portion of the circle x2 + y2 = 64 which is exterior to the parabola y2 = 12x, is

  • 8π - 3 sq units

  • 1638 - 3 sq units

  • 1638π - 3 sq units

  • None of the above


100.

For which of the followmg value of m, is the area of the region bounded by the curve y = x - x2 and the line y = mx equals to 92 ?

  • - 4

  • - 2

  • 2

  • - 4


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