Mathematics

Mathematics

Problem

For any continuous function gg on [p,q][p,q] (p<q)(p<q), which one of the following relations is always true? a) ∫qpg(x) dx=∣∫pqg(x) dx∣\displaystyle \int_{q}^{p} g(x)\,dx = \left|\int_{p}^{q} g(x)\,dx\right| b) ∫qpg(x) dx=−∫pqg(x) dx\displaystyle \int_{q}^{p} g(x)\,dx = -\int_{p}^{q} g(x)\,dx c) ∫qpg(x) dx=∫pqg(x) dx\displaystyle \int_{q}^{p} g(x)\,dx = \int_{p}^{q} g(x)\,dx d) ∫qpg(x) dx=12∫pqg(x) dx\displaystyle \int_{q}^{p} g(x)\,dx = \dfrac{1}{2}\int_{p}^{q} g(x)\,dx

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