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It appears that the image contains a problem asking for the computation of numerical estimates of an integral using the left-endpoints \( L_6 \), right-endpoints \( R_6 \), and midpoints \( M_6 \) for six subintervals. These methods are typically used to approximate the area under a curve or an integral.

Let me clarify what these terms mean and how they relate to the problem:

1. **Left-Endpoint Estimate \( L_6 \):**
   This method takes the left-endpoints of each subinterval to calculate the approximate area under the curve. The formula is:
   \[
   L_n = \sum_{i=1}^{n} f(x_i) \cdot \Delta x
   \]
   where \( f(x_i) \) is the function value at the left endpoint of each subinterval, and \( \Delta x \) is the width of each subinterval.

2. **Right-Endpoint Estimate \( R_6 \):**
   This method uses the right-endpoints of each subinterval to calculate the approximate area. The formula is:
   \[
   R_n = \sum_{i=1}^{n} f(x_{i+1}) \cdot \Delta x
   \]
   where \( f(x_{i+1}) \) is the function value at the right endpoint of each subinterval.

3. **Midpoint Estimate \( M_6 \):**
   The midpoint approximation uses the midpoint of each subinterval. The formula is:
   \[
   M_n = \sum_{i=1}^{n} f\left(\frac{x_i + x_{i+1}}{2}\right) \cdot \Delta x
   \]
   where the value of the function is evaluated at the midpoint of each subinterval.

In your image, you will need to compute these approximations based on the given function and interval. To proceed with solving, please provide the function and the interval over which you need to approximate the integral. If there are any specific values for the function or interval boundaries, that information will be crucial to continue.

Would you like me to provide the formula for each approximation method in more detail, or do you want help with the setup?

### Relative questions:
1. What function are we approximating the area for in this problem?
2. What is the interval over which we are computing the integral?
3. What is the step size \( \Delta x \) for the subintervals?
4. Do you have any graph or data table for the function values at the endpoints or midpoints?
5. Do you want to understand how underestimates or overestimates relate to concavity or function behavior?

**Tip:** When deciding between underestimates and overestimates, always consider whether the function is increasing or decreasing on the interval.

The image contains a problem asking to compute the numerical estimates of an integral using left-endpoints (L6), right-endpoints (R6), and midpoints (M6) for six subintervals.

Learn how to approximate an integral using numerical methods like left-endpoints (L6), right-endpoints (R6), and midpoints (M6) for 6 subintervals. This problem involves basic calculus concepts and formulas, including Σ f(x) * Δx.

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