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  • Confused! kindly explain, - Integral Calculus - JEE Main-4

\int_{-\Pi /2}^{\Pi /2}\frac{cosx}{1+e^{x}}dx  is equal to?

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    -1

  • Option 4)

    -2

 

Answers (1)

best_answer

As we learnt

Properties of definite integration -

If f\left ( x \right ) is an EVEN function of x: then integral of the function from - a to a is the same as twice the integral of the same function from o to a.

\int_{-a}^{a}f(x)dx= 2\left \{ \int_{o}^{a} f(x)dx\right \}

 

- wherein

Check even function f(-x)=f(x) and symmetrical about y axis.

 

 

 

I=\int_{-\pi/2}^{\pi/2}\frac{\cos x}{1+e^{x}}dx= \int_{0}^{\pi/2}\left (\frac{\cos x}{1+e^{x}}+\frac{\cos (-x)}{1+e^{x}} \right )dx=\int_{0}^{\pi/2}\cos xdx =\left [ \sin x\right ]_{0}^{\pi/2}=1


Option 1)

1

Option 2)

2

Option 3)

-1

Option 4)

-2

Posted by

gaurav

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