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  • I have a doubt, kindly clarify. - Integral Calculus - JEE Main-15

Evaluate  \int_{0}^1{}\frac{e^{2x}}{e+2x}dx

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    1/2

  • Option 4)

    1/4

 

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 can be rewritten as \int_{0}^{1}\frac{\frac{e^{2x}}{e^{x}}}{\frac{e}{e^{x}}+\frac{e^{2x}}{e^{x}}}dx

I\Rightarrow \int_{0}^{1}\frac{e^{x}}{e^{1-x}+e^{x}}dx

So I=1/2


Option 1)

1

Option 2)

2

Option 3)

1/2

Option 4)

1/4

Posted by

prateek

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