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  • I have a doubt, kindly clarify. - Integral Calculus - JEE Main-14

Evaluate \int_{0}^{\pi/2}\frac{e^{\sin x}}{e^{\sin x}+e^{\cos x}}dx

  • Option 1)

    \pi

  • Option 2)

    \pi/4

  • Option 3)

    \pi/2

  • Option 4)

    \pi/8

 

Answers (1)

best_answer

As we learnt 

 

Properties of Definite Integration -

 

\int_{0}^{a}\, f(x)dx= \int_{0}^{a} f(a-x)dx

Thus \int_{0}^{a}\, \frac{f(x)}{f(x)+f(a-x)}dx= \frac{a}{2}

-

 

 

 

I=f(x)= \int_{0}^{\pi /2}\frac{e^{sinx}}{e^{sinx}+e^{cosx}}dx

I=f(\pi /2-x)= \int_{0}^{\pi /2}\frac{e^{cosx}}{e^{sinx}+e^{cosx}}dx

Thus 

2I=f(\pi /2-x)= \int_{0}^{\pi /2}dx\Rightarrow I=\pi/4


Option 1)

\pi

Option 2)

\pi/4

Option 3)

\pi/2

Option 4)

\pi/8

Posted by

gaurav

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