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  • Confused! kindly explain, - Integral Calculus - JEE Main-16

Integrate \int_{\pi/3}^{\pi/6}\frac{f\left ( sinx \right )}{f\left ( sinx \right )+f\left ( cosx \right )}dx

  • Option 1)

    \pi/6

  • Option 2)

    \pi/12

  • Option 3)

    \pi/24

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt 

 

Properties of Definite Integration -

 

\int_{a}^{b}f\left ( x \right )dx= \int_{a}^{b}f\left ( a+b-x \right )dx

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

-

 

 Here f(sinx)=f(cos\left ( \frac{\pi}{2}-x \right ))

Thus I=\frac{1}{2}\left ( \frac{\pi}{6}-\frac{\pi}{3} \right )=\frac{\frac{-\pi}{6}}{2}= \frac{-\pi}{12}

 


Option 1)

\pi/6

Option 2)

\pi/12

Option 3)

\pi/24

Option 4)

none of these

Posted by

gaurav

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