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JEE Main2008MathematicsDefinite IntegrationActual

Let I = ₀^1 x x dx and J = ₀^1 x x dx . Then which one of the following is true?

Options

  1. AI > 2 3 and J >2
  2. BI < 2 3 and J < 2
  3. CI 2
  4. DI> 2 3 and J < 2

Correct answer

B. I < 2 3 and J < 2

Step-by-step solution

aligned & I = ₀^1 x x dx < ₀^1 x x dx = ₀^1 x dx = . 2 3 x ^ 3 / 2 |₀ ^1= 2 3 & I < 2 3 & ~J = ₀^1 x x dx < ₀^1 1 x dx = .2 x |₀ ^1=2 & J 2 . aligned

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