Definite integral as a limit of Riemann sums

Practice Questions

AP Calculus AB › Definite integral as a limit of Riemann sums

Questions

3

1

is a continuous function on the interval $\left [ 1,10 \right ]$ and is differentiable on the open interval $\left ( 1,10 \right )$ . If , then which of the following statements MUST be true:

2

You may use one or both of the following summation formulas:

$\sum_{i=1}^n i = \frac{n(n+1)}{2}$

$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$

Express the following definite integral as a limit of Riemman Sums. Then evaluate the integral by evaluating the limit.

$\int_1^2 (x-1)^2dx$

3

True or False: If is a negative-valued function for all , $\int_0^1 f(x) dx <0$ .

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