int_{-3}^{3} frac{x^2 sin x}{1 + x^6} , dx = | vedclass

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(C) Let $f(x) = \frac{x^2 \sin x}{1 + x^6}$.Check if the function is even or odd by evaluating $f(-x)$:$f(-x) = \frac{(-x)^2 \sin(-x)}{1 + (-x)^6} = \

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(C) Let $f(x) = \frac{x^2 \sin x}{1 + x^6}$.Check if the function is even or odd by evaluating $f(-x)$:$f(-x) = \frac{(-x)^2 \sin(-x)}{1 + (-x)^6} = \frac{x^2 (-\sin x)}{1 + x^6} = -\frac{x^2 \sin x}{1 + x^6} = -f(x)$.Since $f(-x) = -f(x)$,the function $f(x)$ is an odd function.Using the property of definite integrals,$\int_{-a}^{a} f(x) \, dx = 0$ if $f(x)$ is an odd function.Therefore,$\int_{-3}^{3} \frac{x^2 \sin x}{1 + x^6} \, dx = 0$.

$\int_{-3}^{3} \frac{x^2 \sin x}{1 + x^6} \, dx = $

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