If I₁ = ∫₀¹ 2^(x²)dx,I₂ = ∫₀¹ 2^(x³)dx, I₃ = ∫₁² 2^(x²)dx and I₄ = ∫₁² 2^(x³)dx then

Integral Calculus: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q3337

JEE Main 2005Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

{I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}dx,\,{I_3} = \int\limits_1^2 {{2^{{x^2}}}dx} } }

and

{I_4} = \int\limits_1^2 {{2^{{x^3}}}dx}

then

JEE Main 2005 · Annual, Paper 1 · Q3337

JEE Main 2005Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

{I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}dx,\,{I_3} = \int\limits_1^2 {{2^{{x^2}}}dx} } }

and

{I_4} = \int\limits_1^2 {{2^{{x^3}}}dx}

then