The value of int_{-100}^{100} frac{x+x^3+x^5} | vedclass

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(C) Let $f(x) = \frac{x+x^3+x^5}{1+x^2+x^4+x^6}$.Check if $f(x)$ is an odd function by evaluating $f(-x)$:$f(-x) = \frac{(-x)+(-x)^3+(-x)^5}{1+(-x)^2+

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(C) Let $f(x) = \frac{x+x^3+x^5}{1+x^2+x^4+x^6}$.Check if $f(x)$ is an odd function by evaluating $f(-x)$:$f(-x) = \frac{(-x)+(-x)^3+(-x)^5}{1+(-x)^2+(-x)^4+(-x)^6} = \frac{-x-x^3-x^5}{1+x^2+x^4+x^6} = -\left(\frac{x+x^3+x^5}{1+x^2+x^4+x^6}\right) = -f(x)$.Since $f(-x) = -f(x)$, the function is an odd function.According to the property of definite integrals, if $f(x)$ is an odd function, then $\int_{-a}^{a} f(x) dx = 0$.Therefore, $\int_{-100}^{100} \frac{x+x^3+x^5}{1+x^2+x^4+x^6} dx = 0$.

The value of $\int_{-100}^{100} \frac{x+x^3+x^5}{1+x^2+x^4+x^6} dx$ is

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