QuestionGiven the function $f(x)=\cos (\pi x)$, compute the right-endpoint (Riemann) sum using $n=3$ on the interval $[0,1]$. $R_{3}=$ help (numbers)

Studdy Solution
Compute the Riemann sum:
The Riemann sum $R_3$ is given by:
$R_3 = \Delta x \left[ f\left(\frac{1}{3}\right) + f\left(\frac{2}{3}\right) + f(1) \right]$
Substitute the values:
$R_3 = \frac{1}{3} \left[ \frac{1}{2} + \left(-\frac{1}{2}\right) + (-1) \right]$
Simplify the expression:
$R_3 = \frac{1}{3} \left[ \frac{1}{2} - \frac{1}{2} - 1 \right]$ $R_3 = \frac{1}{3} \times (-1)$ $R_3 = -\frac{1}{3}$
The value of the right-endpoint Riemann sum $R_3$ is:
$\boxed{-\frac{1}{3}}$