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…
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
$I_2>I_1$
$I_1>I_2$
$I_3=I_4$
$I_3>I_4$
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}
$