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  • Need clarity, kindly explain! Which of the integrals is always positive?

Which of the integrals is always positive?

  • Option 1)

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

  • Option 2)

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

  • Option 3)

    \int_{a}^{b}e^{-x}dx

  • Option 4)

    \int_{a}^{b} sgn (x)dx

 

Answers (1)

best_answer

As we have learnt,

 

Properties of Definite Integration -

If f(x)\geqslant 0 for all

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

\int_{a}^{b}f\left ( x \right )dx\geqslant 0

-

 

 e^{-x} > 0, \forall x \epsilon \mathbb{R}

thus   \int_{a}^{b}e^{-x}dx > 0, \forall (a, b)\; \epsilon \;\mathbb {R}

 


Option 1)

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

Option 2)

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

Option 3)

\int_{a}^{b}e^{-x}dx

Option 4)

\int_{a}^{b} sgn (x)dx

Posted by

gaurav

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