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JEE Main201815 Apr 2018Evening ShiftMathematicsDefinite IntegrationActual

If I₁= ₀^1 e^ -x ^2 x d x ; I₂= ₀^1 e^ -x^2 ^2 x d x and I₃= ₀^1 e^ -x^3 d x ; then

Options

  1. AI₂>I₃>I₁
  2. BI₃>I₁>I₂
  3. CI₂>I₁>I₃
  4. DI₃>I₂>I₁

Correct answer

D. I₃>I₂>I₁

Step-by-step solution

Given: aligned &I₁= ₀^1 e^ -x ^2 x d x &I₂= ₀^1 e^ -x^2 ^2 x d x and &I₃= ₀^1 e^ -x^3 d x & For x (0,1) & x>x^2 or -x x^3 or -x^2 e^ -x^2 >e^ -x & I₃>I₂>I₁ aligned

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