AP Calculus AB 6.3 Riemann Sums Question Bank

Interpret a limiting Riemann sum as a definite integral, identify its bounds and integrand, and use the limit expression to determine the integral value.

Exam points

interpret a Riemann sum as accumulated area or a definite integral
translate between summation notation, limits and definite-integral notation

[Maximum number: 1]

For a certain continuous function f, the right Riemann sum approximation of $\int_{0}^{2} f(x) d x$ with n subintervals of equal length is $\frac{2(n+1)(3 n+2)}{n^{2}}$ for all n. What is the value of $\int_{0}^{2} f(x) d x$ ?

$Graph of $f$$

Graph of $f$

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LIM-5.B—Interpret the limiting case of the Riemann sum as a definite integral question 1