Definite Integrals and Function Symmetry
Let $$t$$ be a function such that $$t(-x) = -t(x)$$ for all $$x$$. If $$\displaystyle\int_1^3 (t(x) + x^2)\,dx = 18$$, then $\displaystyle\int_{-3}^{-1} (t(x) + x^2),dx =\ ?
Let $$t$$ be a function such that $$t(-x) = -t(x)$$ for all $$x$$. If $$\displaystyle\int_1^3 (t(x) + x^2)\,dx = 18$$, then $$\displaystyle\int_{-3}^{-1} (t(x) + x^2)\,dx =\ ?$$
A
$$\displaystyle -\frac{2}{3}$$
B
$$\displaystyle 18$$
C
$$\displaystyle -18$$
D
$$\displaystyle \frac{2}{3}$$
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