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AP EAMCET202421 May 2024Morning ShiftMathematicsArea Under CurvesActual

The area of the region under the curve y=| x- x| , 0 x 2 and above x -axis, is (in square units)

Options

  1. A2 2
  2. B2 2 -1
  3. C2( 2 -1)
  4. D2( +1 )

Correct answer

C. 2( 2 -1)

Step-by-step solution

aligned & y=| x- x|, 0 x 2 & Now, Area = ₀^ 2 | x- x| d x & = ₀^ 4 ( x- x) d x+ _ 4 ^ 2 ( x- x) d x & =[ x+ x]₀^ 4 -[ x+ x]_ 4 ^ 2 & = 1 2 + 1 2 -1- [1- 1 2 - 1 2 ]=2( 2 -1) aligned

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