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  • I have a doubt, kindly clarify. Which of the following integrals has the greatest value in the interval [0, 1]

Which of the following integrals has the greatest value in the interval [0, 1]

  • Option 1)

    \int_{a}^{b}x^{2}dx

  • Option 2)

    \int_{a}^{b}\sqrt{x}dx

  • Option 3)

    \int_{a}^{b}xdx

  • Option 4)

    \int_{a}^{b}x^{4}dx

 

Answers (1)

best_answer

As we have learnt,

 

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

-

 

 In interval [0, 1]

x^{4} < x^{2}< x^{1}< \sqrt{x}

 


Option 1)

\int_{a}^{b}x^{2}dx

Option 2)

\int_{a}^{b}\sqrt{x}dx

Option 3)

\int_{a}^{b}xdx

Option 4)

\int_{a}^{b}x^{4}dx

Posted by

gaurav

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