If ${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$ ${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$ and ${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$ then

Question

If ${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$

${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$ and

${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$ then

I₂ > I₃ > I₁