Mathematics

Mathematics

Problem

For a continuous rate function rr on [a,b][a,b], which of the following conditions is sufficient to guarantee that ∫abr(x) dx=∫ab∣r(x)∣ dx\displaystyle \int_{a}^{b} r(x)\,dx = \int_{a}^{b} |r(x)|\,dx? a) r(x)≤0r(x)\le 0 for all xx in [a,b][a,b] b) ∫abr(x) dx=0\displaystyle\int_{a}^{b} r(x)\,dx = 0 c) r(x)≥0r(x)\ge 0 for all xx in [a,b][a,b] d) r(x)r(x) attains both positive and negative values on [a,b][a,b]

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