10. Approximate the area of the region bounded by the graphs of the equations given below using rectangles and 4 equal length sub-intervals, once with a "left" approximation and once with a "right" approximation (as indicated in "take- home" problem 1). Compute the average of the two approximations to improve your approximation of the area of the region. y=0, y=1+, x=-1, x=3 x2 3'
10. Approximate the area of the region bounded by the graphs of the equations given below using rectangles and 4 equal length sub-intervals, once with a "left" approximation and once with a "right" approximation (as indicated in "take- home" problem 1). Compute the average of the two approximations to improve your approximation of the area of the region. y=0, y=1+, x=-1, x=3 x2 3'
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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
Transcribed Image Text:**Problem 10: Area Approximation Using Rectangles**
Objective: Approximate the area of the region bounded by the graphs of the given equations using rectangles and four equal-length sub-intervals.
Instructions:
1. Perform the approximation once using a "left" endpoint approach and once using a "right" endpoint approach (as indicated in "take-home" problem 1).
2. Compute the average of the two approximations to improve your estimation of the area of the region.
**Equations and Boundaries:**
- \( y = 0 \)
- \( y = 1 + \frac{x^2}{3} \)
- \( x = -1 \)
- \( x = 3 \)
**Tasks:**
- Divide the interval between \( x = -1 \) and \( x = 3 \) into 4 equal parts.
- Use the left endpoint to calculate the height of the rectangles for the "left" approximation.
- Use the right endpoint to calculate the height for the "right" approximation.
- Calculate the average of both approximations for a more accurate estimation.
**Note:**
This exercise involves understanding the concept of Riemann sums and the midpoint, trapezoidal, or Simpson's rules could serve as alternative methods for approximating areas under curves.
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