Let f(x) = int frac{x^2-3x+2}{x^4+1} , dx. Th | vedclass

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(C) Given $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$.By the Fundamental Theorem of Calculus,the derivative is $f'(x) = \frac{x^2-3x+2}{x^4+1}$.For the

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$(1, 2)$

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(C) Given $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$.By the Fundamental Theorem of Calculus,the derivative is $f'(x) = \frac{x^2-3x+2}{x^4+1}$.For the function $f(x)$ to be decreasing,we must have $f'(x) Since $x^4+1 > 0$ for all real $x$,the condition $f'(x) Factoring the quadratic expression,we get $(x-1)(x-2) The roots of the quadratic are $x=1$ and $x=2$.Testing the intervals,the expression $(x-1)(x-2)$ is negative when $x \in (1, 2)$.Therefore,the function decreases in the interval $(1, 2)$.

Let $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$. Then the function decreases in the interval:

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