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\int_{-\pi }^{\pi }\; \frac{2x(1+sin\, x)}{1+cos^{2}x}\: dx\; is

  • Option 1)

    \pi ^{2}/4\;

  • Option 2)

    \; \pi ^{2}\;

  • Option 3)

    \; 0\; \;

  • Option 4)

    \; \pi /2

 

Answers (1)

As we learnt in 

 

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.