If I₁ = ∫₀¹ e⁻ˣ cos ²x 1mu dx; I₂ = ∫₀¹ e^(- x²) cos ²x 1mu dx and I₃ = ∫₀¹ e^(- x³) dx; then

Integral Calculus: JEE Main 2018 Mathematics question

JEE Main 2018 · 15 Apr, Evening shift · Q3361

JEE Main 201815 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

{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

JEE Main 2018 · 15 Apr, Evening shift · Q3361

JEE Main 201815 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

{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