If ${I_1} = \mathop \smallint \nolimits_0^1 \,\,{2^x}^2\;\,dx,\;\,\,{I_2} = \mathop \smallint \nolimits_0^1 \,\,{2^x}^3\;\,dx,\;\,\,{I_3} = \mathop \smallint \nolimits_1^2 \,\,{2^x}^2\;\,dx\,\,\;{\rm{and}}\,\,{I_4} = \mathop \smallint \nolimits_1^2 \,\,{2^x}^3\;\,dx$, then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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{I_1} = \int \nolimits_0^1 \,\,{2^x}^2\;\,dx,\;\,\,{I_2} = \int \nolimits_0^1 \,\,{2^x}^3\;\,dx,\;\,\,{I_3} = \int \nolimits_1^2 \,\,{2^x}^2\;\,dx\,\,\;\mathrm{and}\,\,{I_4} = \int \nolimits_1^2 \,\,{2^x}^3\;\,dx

, then

View answer and explanation

Correct option: C

{I_1} > {I_2}

Option D (I2 < I1) is correct because for x in [0, 1], 2^(x³) < 2^(x²), implying that the integral I2 is less than I1.

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