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Function Symmetry and Definite Integrals
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Let $$w$$ be a function such that $$w(x) + w(-x) = 8$$ for all $$x$$. If $$\displaystyle\int_0^3 w(x)\,dx = 21$$, then $\displaystyle\int_{-3}^{3} w(x),dx =\ ?

Let $$w$$ be a function such that $$w(x) + w(-x) = 8$$ for all $$x$$. If $$\displaystyle\int_0^3 w(x)\,dx = 21$$, then $$\displaystyle\int_{-3}^{3} w(x)\,dx =\ ?$$

A

$$\displaystyle 24$$

B

$$\displaystyle 48$$

C

$$\displaystyle 42$$

D

$$\displaystyle 21$$

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