Use reiman sum to estimate the area under the graph of y=xPon Co6] Use left endpoinb with three rectardes (n=3) Adsaw the correct with Xaxis corsechy labeled. graph of the funchion on the xy phne Computatian of Ax. Numbexline with beginig,ending and all goidpoins. Compute the area a for the three rectangles. and Compute the estimatien.
Use reiman sum to estimate the area under the graph of y=xPon Co6] Use left endpoinb with three rectardes (n=3) Adsaw the correct with Xaxis corsechy labeled. graph of the funchion on the xy phne Computatian of Ax. Numbexline with beginig,ending and all goidpoins. Compute the area a for the three rectangles. and Compute the estimatien.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Title: Calculating Area Under a Curve Using Riemann Sums**
**Objective:**
Estimate the area under the graph of the function \( y = x^2 \) on the interval \([0, 6]\) using left endpoints and three rectangles (n=3).
**Instructions:**
1. **Draw the Graph:**
- Accurately sketch the graph of \( y = x^2 \).
- Ensure the x-axis is correctly labeled with appropriate values.
2. **Draw the Rectangles:**
- Illustrate the left Riemann sum using three rectangles.
- Begin by plotting the function on the xy-plane.
- Use left endpoints to draw the rectangles under the curve.
3. **Calculate \( \Delta x \):**
- Determine the width of each rectangle, \( \Delta x \).
- Compute based on the interval \([0, 6]\) divided into 3 parts.
4. **Number the Grid Points:**
- Ensure the number line begins at 0 and ends at 6.
- Mark all grid points that are relevant to the calculation.
5. **Compute Areas:**
- Calculate the area of each rectangle.
- Sum these areas to estimate the total area under the curve.
- Present the final estimation clearly.
**Outcome:**
By following the steps above, you will learn to approximate the area under a curve using the Riemann sum method. This technique is foundational for understanding the basics of integral calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e8b0010-4aed-4d57-b920-96d0bf9eca5d%2Ffd1bb8cf-d752-403e-b278-c5d578c34e90%2Fa7brw7n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Area Under a Curve Using Riemann Sums**
**Objective:**
Estimate the area under the graph of the function \( y = x^2 \) on the interval \([0, 6]\) using left endpoints and three rectangles (n=3).
**Instructions:**
1. **Draw the Graph:**
- Accurately sketch the graph of \( y = x^2 \).
- Ensure the x-axis is correctly labeled with appropriate values.
2. **Draw the Rectangles:**
- Illustrate the left Riemann sum using three rectangles.
- Begin by plotting the function on the xy-plane.
- Use left endpoints to draw the rectangles under the curve.
3. **Calculate \( \Delta x \):**
- Determine the width of each rectangle, \( \Delta x \).
- Compute based on the interval \([0, 6]\) divided into 3 parts.
4. **Number the Grid Points:**
- Ensure the number line begins at 0 and ends at 6.
- Mark all grid points that are relevant to the calculation.
5. **Compute Areas:**
- Calculate the area of each rectangle.
- Sum these areas to estimate the total area under the curve.
- Present the final estimation clearly.
**Outcome:**
By following the steps above, you will learn to approximate the area under a curve using the Riemann sum method. This technique is foundational for understanding the basics of integral calculus.
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