Subjects calculus

Riemann Sum Accfca

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Riemann Sum Accfca


1. The problem asks to use the Riemann sum to approximate the integral of a function over an interval. 2. The Riemann sum formula is $$S_n = \sum_{i=1}^n f(x_i^*) \Delta x$$ where $\Delta x = \frac{b-a}{n}$ is the width of each subinterval, and $x_i^*$ is a sample point in the $i$th subinterval. 3. To apply the Riemann sum, first identify the function $f(x)$, the interval $[a,b]$, and the number of subintervals $n$. 4. Calculate $\Delta x = \frac{b-a}{n}$. 5. Choose the sample points $x_i^*$ in each subinterval (left endpoint, right endpoint, or midpoint). 6. Evaluate $f(x_i^*)$ for each $i$. 7. Compute the sum $S_n = \sum_{i=1}^n f(x_i^*) \Delta x$. 8. This sum approximates the definite integral $\int_a^b f(x) \, dx$. Without the specific function and interval from the "above question," this is the general method to use the Riemann sum. If you provide the function and interval, I can compute the Riemann sum explicitly.