Q110 / 225 · JEE Main 2005 · Mathematics

If $\mathrm{I}_1=\int_0^1 2^{x^2} d x, I_2=\int_0^1 2^{x^3} d x, I_3=\int_1^2 2^{x^2} d x$ and $I_4=\int_1^2 2^{x^3} d x$ then

  • A
    $I_2>I_1$
  • Correct answer
    B
    $I_1>I_2$
  • C
    $I_3=I_4$
  • D
    $I_3>I_4$

Solution

$$ \begin{aligned} & l_1=\int_0^1 2^{x^2} d x, l_2=\int_0^1 2^{x^3} d x, I_3=\int_0^1 2^{x^2} d x, I_4=\int_0^1 2^{x^3} d x \\ & \forall 0 < x < 1, x^2>x^3 \\ & \Rightarrow \int_0^1 2^{x^2} d x>\int_0^1 2^{x^3} d x \\ & \Rightarrow I_1>I_2 . \end{aligned} $$

Hence, the correct answer is option: 'B'.

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