If ${I_1} = \mathop \smallint \limits_0^1 \,{2^{{x^2}}}\,dx,\,\;{I_2} = \mathop {\smallint \,}\limits_0^1 {2^{{x^3}}}\,dx,\;\,{I_3} = \mathop \smallint \limits_1^2 \,{2^{{x^2}}}dx\,\,{\rm{and}}\,\,{I_4} = \mathop \smallint \limits_1^2 \,{2^{{x^3}}}\,dx$ Then

${I_2} > {I_1}$ and ${I_3} > {I_4}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

{I_1} = \int \limits_0^1 \,{2^{{x^2}}}\,dx,\,\;{I_2} = \mathop {\int \,}\limits_0^1 {2^{{x^3}}}\,dx,\;\,{I_3} = \int \limits_1^2 \,{2^{{x^2}}}dx\,\,\mathrm{and}\,\,{I_4} = \int \limits_1^2 \,{2^{{x^3}}}\,dx

Then

View answer and explanation

Correct option: A

{I_1} > {I_2}

and

{I_4} > {I_3}

Option C (

{I_1} > {I_2}

and

{I_3} > {I_4}

) is correct because for 0 < x < 1, x² > x³, and for 1 < x < 2, x³ > x².

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