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Manipal MET2011MathematicsDefinite Integration

The value of ₀^ / 2 | x- x| d x is

Options

  1. A0
  2. B2( 2 -1)
  3. C2 -1
  4. D2( 2 +1)

Correct answer

B. 2( 2 -1)

Step-by-step solution

aligned & ₀^ / 2 | x- x| d x & = ₀^ / 4 -( x- x) d x + _ / 4 ^ / 2 -( x- x) d x aligned aligned & aligned = & -[- x- x]₀^ / 4 +[- x- x]_ / 4 ^ / 2 = & - [- 1 2 - 1 2 +1 ] + [-0-1+ ( 1 2 + 1 2 ) ] = & 2 -1-1+ 2 = & 2( 2 -1) aligned aligned

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