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Question Number 7932 by tawakalitu last updated on 24/Sep/16

Commented by sou1618 last updated on 25/Sep/16

$$setf\left(x\right)=\frac{sinx}{1+x^2+x^4}$$$$f(-x)=\frac{sin(-x)}{1+{(-x)}^2+{(-x)}^4}=-f\left(x\right)$$$$so$$$$f(-x)+f\left(x\right)=0$$$$\iff {\int }_0^{1}f(-x)+f\left(x\right)dx=0$$$$\iff {\int }_0^{-1}\frac{-sinx}{1+x^2+x^4}dx+{\int }_0^1\frac{sinx}{1+x^2+x^4}dx=0$$$$\iff -{\int }_{-1}^0\frac{-sinx}{1+x^2+x^4}dx+{\int }_0^1\frac{sinx}{1+x^2+x^4}dx=0$$$$\iff {\int }_{-1}^1\frac{sinx}{1+x^2+x^4}dx=0$$$$\iff {\int }_{-1}^1\frac{sinx}{1+x^2+x^4}dx=0$$

Commented by tawakalitu last updated on 25/Sep/16

$$Thankssomuchsir.$$

Answered by prakash jain last updated on 02/Oct/16

$$\mathrm{answer}\mathrm{in}\mathrm{comments}$$

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