If f ' g' for all a

Question

If f ' > g' for all a < x < b then the right-hand Riemann sum approximation of $\int_{a}^{b} f(x) d x$ will have smaller error than the right-hand Riemann sum for $\int_{a}^{b} g(x) d x$ .

Quizplus · Accepted Answer

The comparison between f(x) and g(x) does not directly determine which right-hand Riemann sum approximation will have a smaller error. The error in Riemann sum approximations depends on the function's behavior (like continuity, differentiability) and how well the partition intervals capture the function's behavior, not just on the magnitude of the function values.

If F ' > G' for All a < X ∫abf(x)dx\int_{a}^{b} f(x) d x∫ab​f(x)dx

If F ' > G' for All a < X $\int_{a}^{b} f(x) d x$