Let \( f \) be a continuous function such that \( \int_{4}^{8} f(x) d x=-6 \) and \( \int_{7}^{4} f(x) d x=-4 \). What is the value of \( \int_{7}^{8} f(x) d x \) ?
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One key property is that the integral from \(a\) to \(b\) of a function is the negative of the integral from \(b\) to \(a\). In mathematical terms, \(\int_{a}^{b} f(x) dx = -\int_{b}^{a} f(x) dx\). Show more…
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$\begin{array}{l}{\text { Suppose that } f(1)=2, f(4)=7, f^{\prime}(1)=5, f^{\prime}(4)=3, \text { and }} \\ {f^{\prime \prime} \text { is continuous. Find the value of } \int_{1}^{4} x f^{\prime \prime}(x) d x}\end{array}$
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