(b) Repeat part (a) using left endpoints. (Round your answer to four decimal places.)

To appropriately address your question regarding using left endpoints, it appears that part (a) involves approximating the area under a curve, typically through a Riemann sum, using left endpoint values. Since the details of part (a) are not provided, I will present a generic solution that demonstrates how to compute a left Riemann sum. Adjust the specific function and intervals accordingly.

1. Break Down the Problem

• Identify the function $f(x)$ you want to integrate.
• Determine the interval $[a, b]$ over which you will integrate.
• Decide on the number of subintervals $n$ to use.

2. Relevant Concepts

• The left Riemann sum $L_n$ is calculated with the following formula: $L_n = \sum_{i=0}^{n-1} f(x_i) \Delta x$ where $\Delta x = \frac{b-a}{n}$ and $x_i = a + i \Delta x$.

3. Analysis and Detail

1. Calculate $\Delta x$: $\Delta x = \frac{b - a}{n}$

2. Determine the left endpoint values: For $i = 0, 1, 2, \ldots, n-1$: $x_i = a + i \Delta x$

3. Evaluate the function at each left endpoint: Calculate $f(x_i)$ for each $i$.

4. Sum up all the function evaluations: $L_n = f(x_0) \Delta x + f(x_1) \Delta x + \ldots + f(x_{n-1}) \Delta x$

4. Verify and Summarize

Conduct the calculations and round the final result to four decimal places. Verify by ensuring the function evaluations are correct and that the sums have been calculated without error.

Final Answer

Assuming the function and values are provided, you can plug in the values to get your final Riemann sum approximation using left endpoints. For an accurate solution, provide the specific function and interval.