7. Is the function $g(x) = \begin{cases} 2x \sin(1/x) - \cos(1/x) & \text{for } x \neq 0\\ 0 & \text{for } x = 0 \end{cases}$ integrable on $[-1, 1]$?\\If so, may we use the Fundamental Theorem of Calculus to find $\int_{-1}^{1} g$?
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To determine if f(x) is integrable on [-1, 1] for r = 0, we need to check if the function is bounded and has a finite number of discontinuities in that interval. Without knowing the specific function f(x), we cannot determine its integrability. Show more…
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