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To solve this problem, we’ll use the upper and lower sums (also called Riemann sums) to approximate the area under the curve given by \( y = \sqrt{1 - x^2} \).

This curve is actually the top half of a circle with radius 1, centered at the origin, so the region under this curve from \( x = -1 \) to \( x = 1 \) represents a semicircle with area \( \frac{\pi}{2} \approx 1.5708 \). However, to approximate this area using Riemann sums, we need to apply the method specified.

### Step-by-Step Solution Outline

1. **Define the Interval and Function:**
   The interval is typically from \( x = -1 \) to \( x = 1 \) (as this is the range for a semicircle). The function to evaluate is:
   \[
   f(x) = \sqrt{1 - x^2}
   \]

2. **Determine Subinterval Width:**
   Let’s denote the number of subintervals as \( n \). Since the problem doesn’t specify the number of subintervals, please confirm this information if available. Otherwise, we can proceed with a general calculation for arbitrary \( n \) or assume a standard value (such as \( n = 4 \)).

   The width of each subinterval \( \Delta x \) is:
   \[
   \Delta x = \frac{1 - (-1)}{n} = \frac{2}{n}
   \]

3. **Calculate Upper and Lower Sums:**
   For the upper and lower sums, we evaluate \( f(x) \) at the endpoints of each subinterval to find the maximum (for the upper sum) and minimum (for the lower sum) function values within each subinterval.

4. **Approximate the Sums:**
   - **Upper Sum**: Sum the areas of rectangles where the height is determined by the maximum value of \( f(x) \) in each subinterval.
   - **Lower Sum**: Sum the areas of rectangles where the height is determined by the minimum value of \( f(x) \) in each subinterval.

5. **Round Answers:**
   Round the upper and lower sums to three decimal places, as specified.

Could you confirm the number of subintervals \( n \)? Once confirmed, I’ll proceed with the calculations.

Use the upper and lower sums to approximate the area of the region under the curve y = √(1 - x^2) with a given number of subintervals (of equal width). Round your answers to three decimal places.

Learn how to use upper and lower Riemann sums to approximate the area under the curve y = √(1 - x^2). This problem involves calculating areas using a specified number of subintervals and rounding the answers to three decimal places. Suitable for calculus students.

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