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KCET2016MathematicsArea Under Curves

Area lying between the curves ( y²=2 x ) and ( y=x )

Options

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

Correct answer

A. ( 2 3 ) sq. units

Step-by-step solution

Given curves, array l y²=2 x (1) y=x (2) array At x=0 and x=2 we have two intersect points, that is, (0,0),(2,2) . Therefore, required area is given by array l ₀²( 2 x -x) d x = [ 2 ( 2 3 x^ 3 / 2 )- x² 2 ]² = ( 2 2 3 (2^ 3 / 2 )- 4 2 ) = 2 3 2²-2= 2 3 sq. units array

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