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The image shows two graphs labeled Figure A and Figure B. Each graph represents the function \( y = \sin(x) \) bounded by \( y = 0 \), \( x = 0 \), and \( x = \pi \). The goal is to approximate the area under the curve using rectangles. Part (a) of the question involves using these rectangles to approximate the area, while part (b) asks how to improve the approximation.

### Part (a) Explanation:
In each graph, rectangles are used to estimate the area under the curve. These types of approximations are typically based on Riemann sums, where the area under the curve is estimated by the sum of the areas of rectangles. The number of rectangles and their placement (e.g., left endpoint, right endpoint, or midpoint) determine the accuracy of the approximation.

For **Figure A**, it looks like three rectangles are used, and for **Figure B**, five rectangles are used.

1. **For Figure A**, with three rectangles, the area should be computed by summing the areas of the three rectangles. The width of each rectangle is \(\pi/3\), and their heights are determined by the value of the function \( \sin(x) \) at specific points (likely midpoints or endpoints of the intervals).
   
2. **For Figure B**, with five rectangles, the width of each rectangle is \( \pi/5 \), and similarly, the height is determined by the function values at the corresponding points.

### Part (b) Explanation:
The question in part (b) asks how to improve the accuracy of the approximation. To obtain a more accurate approximation, the key is to **increase the number of rectangles**. By increasing the number of rectangles, the width of each rectangle becomes smaller, and the approximation becomes closer to the true area under the curve. This is essentially what happens when we take the limit as the number of rectangles approaches infinity, which leads to the integral of the function.

Let me know if you'd like help calculating the exact areas for each figure or if you have any specific questions!

Here are 5 related questions:
1. What is a Riemann sum, and how is it used to approximate area under a curve?
2. What is the difference between left endpoint, right endpoint, and midpoint Riemann sums?
3. How does increasing the number of rectangles improve the accuracy of the approximation?
4. Can you explain how the trapezoidal rule compares to using rectangles for approximating area?
5. What is the integral of \( \sin(x) \) from 0 to \( \pi \), and how does it relate to this problem?

**Tip**: Increasing the number of subdivisions (rectangles) reduces the error in approximating the area under the curve, moving the approximation closer to the exact value given by the definite integral.

Use the rectangles in each graph to approximate the area of the region bounded by y = sin(x), y = 0, x = 0, and x = π.

Learn how to approximate the area under the curve y = sin(x) using Riemann sums. This problem involves calculating areas using rectangles and understanding how increasing the number of rectangles improves the accuracy of the approximation. Suitable for students in Grades 11-12.

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