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COMEDK202510 May 2025Morning ShiftMathematicsDefinite IntegrationActual

₀^ e^ x e^ x +e^ - x d x is equal to

Options

  1. A2
  2. B2
  3. C4

Correct answer

A. 2

Step-by-step solution

Let I = ₀^ e^ x e^ x + e^ - x dx . Using the property ₀^a f(x) dx = ₀^a f(a-x) dx , we have: I = ₀^ e^ ( -x) e^ ( -x) + e^ - ( -x) dx Since ( -x) = - x , the integral becomes: I = ₀^ e^ - x e^ - x + e^ x dx Adding the two expressions for I : 2I = ₀^ ( e^ x e^ x + e^ - x + e^ - x e^ x + e^ - x ) dx 2I = ₀^ e^ x + e^ - x e^ x + e^ - x dx 2I = ₀^ 1 dx = I = 2 Answer: 2

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