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AP EAMCET202318 May 2023Morning ShiftMathematicsDefinite IntegrationActual

If ₀^ 2 |x x| d x=k , then k=

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

₀^ 2 |x x| d x=k ...(i) Let I = ₀^ 2 |x x| d x= ₀^ 2 x| x| d x x>0 = [ ₀^ x x d x- _ ^ 2 x x d x ] aligned & =[-x x]₀^ + [ ₀^ 1 x d x ] & -[-x x]_ ^ 2 - [ _ ^ 2 x d x ] aligned aligned & = + ₀^ 2 x d x- _ 2 ^ x d x+[2 + ]^ & - _ ^ 3 / 2 x d x+ _ 3 / 2 ^ 2 x d x aligned =4 +1-1+1-1=4 I=4 ₀^ 2 |x x| d x=4 ....(ii) From (i) and (ii), k=4

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