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COMEDK20269 May 2026Evening ShiftMathematicsDefinite IntegrationActual

₀^ /2 3 x + 4 x x + x , dx =

Options

  1. A7 2
  2. B4
  3. C7 4
  4. D7

Correct answer

C. 7 4

Step-by-step solution

Let I = ₀^ /2 3 x + 4 x x + x , dx Using the definite integral property ₀^a f(x) , dx = ₀^a f(a-x) , dx , we get: I = ₀^ /2 3 ( /2 - x) + 4 ( /2 - x) ( /2 - x) + ( /2 - x) , dx I = ₀^ /2 3 x + 4 x x + x , dx Adding the two equations for I : 2I = ₀^ /2 3 x + 4 x + 3 x + 4 x x + x , dx 2I = ₀^ /2 7( x + x) x + x , dx 2I = ₀^ /2 7 , dx 2I = 7[x]₀^ /2 = 7 2 I = 7 4 Answer: 7 4

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