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COMEDK202510 May 2025Evening ShiftMathematicsDefinite IntegrationActual

₀^ 2 ( 5+4 x 5+4 x ) d x=

Options

  1. A2
  2. B-2
  3. C0
  4. D3 4

Correct answer

C. 0

Step-by-step solution

Let I = ₀^ 2 ( 5 + 4 x 5 + 4 x ) dx . Using the property ₀^ a f(x) dx = ₀^ a f(a - x) dx , we have: I = ₀^ 2 ( 5 + 4 ( 2 - x) 5 + 4 ( 2 - x) ) dx I = ₀^ 2 ( 5 + 4 x 5 + 4 x ) dx I = ₀^ 2 ( ( 5 + 4 x 5 + 4 x )⁻¹ ) dx I = - ₀^ 2 ( 5 + 4 x 5 + 4 x ) dx I = -I 2I = 0 I = 0 . Answer: 0

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