Let be a continuous function on the interval

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Let gg be a continuous function on the interval [2,5][2,5]. It is known that ∫25g(x) dx=7.\int_{2}^{5} g(x)\,dx = 7. (a) Determine ∫52g(x) dx\int_{5}^{2} g(x)\,dx. (b) Explain why the sign of your answer in part (a) is appropriate when the definite integral is interpreted as the signed area between the graph of gg and the xx–axis on the interval [2,5][2,5]. Be explicit about the role of the limits of integration.

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