Question

If $I_1={\int }_0^1{2}^{x^2}dx,I_2={\int }_0^1{2}^{x^3}dx,I_3={\int }_1^2{2}^{x^2}dx$ and $I_4={\int }_1^2{2}^{x^3}dx$ then

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

Answer 1

The correct option is C $I_1>I_2$

For $0<x<1\Rightarrow x^2>x^3\Rightarrow 2^{x^2}>2^{x^3}\Rightarrow I_1>I_2$
And for $1<x<2\Rightarrow x^3>x^2\Rightarrow 2^{x^3}>2^{x^2}\Rightarrow I_4>I_3$