The area of the region described by

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151.

The area of the region described by(x, y)/x2 + y  1 and y  1 - x is

  • π2 - 23

  • π2 + 23

  • π2 + 43

  • π2 - 43


C.

π2 + 43

Required area

= 2 - 101 - x2dx + 011 - x2dx= x21 - x2 + 12sin-1x- 10 + 2 - 231 - x3201= π2 + 43


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152.

Consider a region R = {(x, y)  R: xy  2x}. If a line y = α divides the area of region R into two equal parts, then which of the following is true ?

  • 3α2 - 8α + 8 = 0

  • α3 - 6α32 - 16 = 0

  • α3 - 6α2 + 16 = 0

  • 2 - 8α32 + 8 = 0


153.

The area in sq unit of the region x, y; 12  y  sinx, 0  x  πis equal to

  • 3 - 2π

  • 3 - π6

  • 3 - π3

  • 3 - π3


154.

The area (in sq. units) of the region A = {x, y) : (x –1) [x]  y  2x, 0  x  2,where [t] denotes the greatest integer function, is :

  • 432 - 12

  • 832 - 1

  • 432 + 1

  • 832 - 12


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155.

The area (in sq. units) of the region A = x, y :x + y  1, 2y2  x :

  • 56

  • 76

  • 13

  • 16


156.

The area (in sq. units) of the region enclosed by the curves y = x2 – 1 and y = 1 – x2 is equal to :

  • 83

  • 72

  • 43

  • 163


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