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Manipal MET2014MathematicsArea Under Curves

The area bounded by y=x| x| and X -axis between x=0 and x=2 is

Options

  1. A2 sq units
  2. B3 sq units
  3. Csq units
  4. D4 sq units

Correct answer

D. 4 sq units

Step-by-step solution

aligned y & =x| x| y & = array c x x, 0 x -x x, x 2 array aligned aligned Required Area & = ₀^ x x+ _ ^ 2 (-x x) d x & =[x(- x)]₀^ - ₀^ (- x) d x - & [ x(- x) ]_ ^ 2 + _ ^ 2 (- x) d x & =[ + x]₀^ +[(2 + )- x]_ ^ 2 = & 4 sq units aligned

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