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JEE Main2005MathematicsDefinite IntegrationActual

If I ₁= ₀^1 2^ x^2 d x, I₂= ₀^1 2^ x^3 d x, I₃= ₁^2 2^ x^2 d x and I₄= ₁^2 2^ x^3 d x then

Options

  1. AI₂>I₁
  2. BI₁>I₂
  3. CI₃=I₄
  4. DI₃>I₄

Correct answer

B. I₁>I₂

Step-by-step solution

aligned & l₁= ₀^1 2^ x^2 d x, l₂= ₀^1 2^ x^3 d x, I₃= ₀^1 2^ x^2 d x, I₄= ₀^1 2^ x^3 d x & 0 x^3 & ₀^1 2^ x^2 d x> ₀^1 2^ x^3 d x & I₁>I₂ . aligned

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