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KCET2017MathematicsDifferentiation

The area of the region bounded by the curve ( y=x² ) and the line ( y=16 ) is

Options

  1. A( 32 3 ) sq. units
  2. B( 256 3 ) sq. units
  3. C( 64 3 ) sq. units
  4. D( 128 3 ) sq. units

Correct answer

B. ( 256 3 ) sq. units

Step-by-step solution

Given curve, y=x² (1) and given line, y=16 (2) Therefore, required area is given by 2 Area of region OAC array l =2 ₀¹⁶ y d y =2 2 3 [y^ 3 2 ]₀¹⁶=2 2 3 (16)^ 3 2 =2 2 3 (4)³= 256 3 array

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