The value of int_{-2}^{2}(a x^{3}+b x+c) d x | vedclass

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(C) Let $I = \int_{-2}^{2}(a x^{3} + b x + c) d x$. We can split the integral as: $I = \int_{-2}^{2} a x^{3} d x + \int_{-2}^{2} b x d x + \int_{-2}^{

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value of $c$

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(C) Let $I = \int_{-2}^{2}(a x^{3} + b x + c) d x$. We can split the integral as: $I = \int_{-2}^{2} a x^{3} d x + \int_{-2}^{2} b x d x + \int_{-2}^{2} c d x$. We know that for an odd function $f(x)$,$\int_{-k}^{k} f(x) d x = 0$. Since $a x^{3}$ and $b x$ are odd functions,$\int_{-2}^{2} a x^{3} d x = 0$ and $\int_{-2}^{2} b x d x = 0$. Thus,$I = 0 + 0 + \int_{-2}^{2} c d x = \int_{-2}^{2} c d x = [c x]_{-2}^{2} = c(2 - (-2)) = 4c$. Therefore,the value of the integral depends only on the value of $c$.

The value of $\int_{-2}^{2}(a x^{3}+b x+c) d x$ depends on the

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