The problem asks to compute an approximate value for $I$ using a Riemann sum with 10 subintervals. It specifies that the subintervals are equidistant and that the left endpoint of each interval is used to evaluate the function. Here is a breakdown of the task:

Steps to Solve:

1. Identify the Interval and Function:

   • The interval of integration and the function $f(x)$ to approximate $I$ are not shown in the extracted image. If you provide those details (or another part of the problem), I can include them in the calculation.

2. Divide the Interval:

   • Split the interval into $n = 10$ equal parts. The width of each subinterval is given by: $\Delta x = \frac{\text{(b - a)}}{n}$

3. Choose Left Endpoints:

   • The left endpoint of the $k$-th subinterval is: $x_k = a + (k-1)\Delta x \quad \text{for } k = 1, 2, \ldots, n.$

4. Evaluate the Riemann Sum:

   • The approximate value of the integral $I$ is: $I \approx \sum_{k=1}^{n} f(x_k) \Delta x$

5. Compute the Sum:

   • Plug in the given function and calculate the sum numerically.

If you share the interval of integration and the function $f(x)$, I can solve the entire problem explicitly. Would you like to proceed?

5 Related Questions:

1. What are Riemann sums, and how do they help in approximating integrals?
2. What is the difference between left, right, and midpoint Riemann sums?
3. How does increasing the number of subintervals affect the approximation?
4. Could this calculation be done with a trapezoidal rule for better accuracy?
5. What are some common errors when implementing numerical integration?

Tip:

Always double-check whether the endpoints and number of subintervals match the chosen numerical method!