Suppose the points $x_{0}, x_{1}, \ldots, x_{n}$ are equally spaced and $\alpha$$=$$x_{0}$$

Question

Suppose the points $x_{0}, x_{1}, \ldots, x_{n}$ are equally spaced and $\alpha$$=$$x_{0}$$<$$x_{1}$$\text { < }$... $<$$x_{n}$$=b$ .What is the formula (in terms of f and the $x_{i}$ 's)for the right Riemann sum approximation to $\int_{a}^{b} f(x) d x$ ?
A) $\sum_{i=a}^{b} f\left(x_{i}\right) \Delta x$
B) $\sum_{i=a+n}^{b+n} f\left(x_{i}\right) \Delta x$
C) $\sum_{i=1}^{n} f\left(x_{i}\right) \Delta x$
D) $\sum_{i=0}^{n-1} f\left(x_{i}\right) \Delta x$

Quizplus · Accepted Answer

The right Riemann sum approximation uses the value of the function at the right end of each subinterval to approximate the integral. Since the points are $x_0, x_1, \ldots, x_n$, and we start from the right of the first interval, the sum should start from $x_1$ and go to $x_n$, making option C correct.

Suppose the Points x0,x1,…,xnx_{0}, x_{1}, \ldots, x_{n}x0​,x1​,…,xn​ Are Equally Spaced And α\alphaα

Suppose the Points $x_{0}, x_{1}, \ldots, x_{n}$ Are Equally Spaced And $\alpha$