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If      I_{1}=\int_{0}^{1}2^{x^{2}}dx,I_{2}=\int_{0}^{1}2^{x^{3}}dx,I_{3}=\int_{1}^{2}2^{x^{2}}dx\; \; and\;\; I_{4}=\int_{1}^{2}2^{x^{3}}dx\; \; then

  • Option 1)

    I_{1}> I_{2}

  • Option 2)

    I_{2}> I_{1}

  • Option 3)

    I_{3}> I_{4}

  • Option 4)

    I_{3}= I_{4}

 

Answers (1)

best_answer

As learnt in concept

Properties of Definite Integration -

If f(x)\geqslant g(x) for

all x\in \left [ a,b \right ] then

\int_{a}^{b}f\left ( x \right )dx\geqslant \int_{a}^{b}g(x)dx

-

 

 Since the limits are (0,1)

x^{2}>x^{3}>x^{4}

Thus, 2^{x^{2}}>2^{x^{3}}

Hence, \int_{0}^{1}2^{x^{2}}dx>\int_{0}^{1}2^{x^{3}}dx

I_{1}>I_{2}


Option 1)

I_{1}> I_{2}

This option is correct

Option 2)

I_{2}> I_{1}

This option is incorrect

Option 3)

I_{3}> I_{4}

This option is incorrect

Option 4)

I_{3}= I_{4}

This option is incorrect

Posted by

perimeter

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