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  • Solve it, Which of the following integrals has greatest value in the interval [1, b] ?

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

  • Option 1)

    \int_{1}^{b}x^{2}dx

  • Option 2)

    \int_{1}^{b}x^{3}dx

  • Option 3)

    \int_{1}^{b}x^{4}dx

  • Option 4)

    \int_{1}^{b}xdx

 

Answers (1)

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

-

 

 Since for x > 1,

x , x^2 < x^3 < x^4

 


Option 1)

\int_{1}^{b}x^{2}dx

Option 2)

\int_{1}^{b}x^{3}dx

Option 3)

\int_{1}^{b}x^{4}dx

Option 4)

\int_{1}^{b}xdx

Posted by

Vakul

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