The value of int_{-2}^{2} (ax^3 + bx + c) dx | vedclass

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(C) We evaluate the definite integral $\int_{-2}^{2} (ax^3 + bx + c) dx$. Using the property of linearity,we can split the integral: $\int_{-2}^{2} ax

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The value of $c$

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(C) We evaluate the definite integral $\int_{-2}^{2} (ax^3 + bx + c) dx$. Using the property of linearity,we can split the integral: $\int_{-2}^{2} ax^3 dx + \int_{-2}^{2} bx dx + \int_{-2}^{2} c dx$. Since $ax^3$ and $bx$ are odd functions and the interval $[-2, 2]$ is symmetric about the origin,$\int_{-2}^{2} ax^3 dx = 0$ and $\int_{-2}^{2} bx dx = 0$. Thus,the integral simplifies to $\int_{-2}^{2} c dx = [cx]_{-2}^{2} = c(2) - c(-2) = 2c + 2c = 4c$. Since the result is $4c$,the value of the integral depends only on the value of $c$.

The value of $\int_{-2}^{2} (ax^3 + bx + c) dx$ depends on

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