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AP EAMCET202421 May 2024Evening ShiftMathematicsDefinite IntegrationActual

₁^5(|x-3|+|1-x|) d x=

Options

  1. A4
  2. B8
  3. C12
  4. D24

Correct answer

C. 12

Step-by-step solution

aligned & |x-3|= cases 3-x, & x 3 x-3, & x 3 cases & and |1-x|=x-1 ; x 1 & I= ₁^5(|x-3|+|1-x|) d x & = ₁^3(3-x+x-1) d x+ ₃^5(x-3+x-1) d x & = ₁^3 2 d x+ ₃^5(2 x-4) d x=4+ [x^2-4 x ]₃^5=12 . aligned

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