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BITSAT2010MathematicsDifferential EquationsActual

The area of the region bounded by the curve (y=x|x|, x )-axis and the ordinates (x=1, x=-1 ) is given by :

Options

  1. Azero
  2. B( 1 3 )
  3. C( 2 3 )
  4. D1

Correct answer

C. ( 2 3 )

Step-by-step solution

The area of the region bounded by the curve (y=f(x) ) and the ordinates (x=a, x=b ) is given by ( Area = | _a^b y d x | ) According to the question, (y=x|x|= cases x^2, & x 0 -x^2, & x Required area (= ) area of region ( OAB + ) area of region ( OCD ) (=2 ) Area of region ( OAB ) (=2 ₀^1 x^2 d x= 2 3 s q ). units

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