Let g be a continuous function on the interval [2,5]. It is known that
∫25g(x)dx=7.
(a) Determine the exact value of ∫52g(x)dx.
(b) Describe, in complete sentences, how the value in part (a) is consistent with the geometric interpretation of a definite integral as signed area. Your explanation should reference the orientation of the interval of integration and the effect of that orientation on the sign of the integral.
(a) Determine ∫52g(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 g and the x–axis on the interval [2,5]. Be explicit about the role of the limits of integration.