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KCET2015MathematicsDifferentiation

Area bounded by ( y=x³, y=8 ) and ( x=0 ) is

Options

  1. A( 2 ) sq. units
  2. B( 14 sq ). units
  3. C( 12 sq ). units
  4. D( 6 ) sq. units

Correct answer

C. ( 12 sq ). units

Step-by-step solution

Given equation, y=x³ (1)y=8 (2)x=0 (3) Now, ( x=y^ 1 / 3 ) So, required area is given by ( ₀⁸ x d y ) [ array l = ₀⁸ y^ 1 / 3 d y= [ 3 4 y^ 4 / 3 ]₀⁸= 3 4 (8^ 4 / 3 ) = 3 4 (2⁴ )=12 array ]

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