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**Graph Description:** The image features a graph with the function \( y = f(x) \) represented by a red curve. There are five green rectangles under the curve along the x-axis, ranging from \( x = 0 \) to \( x = 4 \). These rectangles illustrate a midpoint approximation for estimating the area under the curve. Each rectangle's height corresponds to the value of the function at the midpoint of its base. **Equation Instructions:** 5. The five rectangles shown represent a midpoint approximation for the area under the curve, \( y = f(x) \). Complete the equation, by writing the formula for the sum of the areas of the rectangles: \[ A \approx \text{Area 1} + \text{Area 2} + \text{Area 3} + \text{Area 4} + \text{Area 5} \] \[ A \approx ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) \] The rectangles' base widths and function evaluation points at each midpoint need to be determined to complete the calculation.

**Graph Description:** The image features a graph with the function \( y = f(x) \) represented by a red curve. There are five green rectangles under the curve along the x-axis, ranging from \( x = 0 \) to \( x = 4 \). These rectangles illustrate a midpoint approximation for estimating the area under the curve. Each rectangle's height corresponds to the value of the function at the midpoint of its base. **Equation Instructions:** 5. The five rectangles shown represent a midpoint approximation for the area under the curve, \( y = f(x) \). Complete the equation, by writing the formula for the sum of the areas of the rectangles: \[ A \approx \text{Area 1} + \text{Area 2} + \text{Area 3} + \text{Area 4} + \text{Area 5} \] \[ A \approx ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) \] The rectangles' base widths and function evaluation points at each midpoint need to be determined to complete the calculation.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Graph Description:** The image features a graph with the function \( y = f(x) \) represented by a red curve. There are five green rectangles under the curve along the x-axis, ranging from \( x = 0 \) to \( x = 4 \). These rectangles illustrate a midpoint approximation for estimating the area under the curve. Each rectangle's height corresponds to the value of the function at the midpoint of its base. **Equation Instructions:** 5. The five rectangles shown represent a midpoint approximation for the area under the curve, \( y = f(x) \). Complete the equation, by writing the formula for the sum of the areas of the rectangles: \[ A \approx \text{Area 1} + \text{Area 2} + \text{Area 3} + \text{Area 4} + \text{Area 5} \] \[ A \approx ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) \] The rectangles' base widths and function evaluation points at each midpoint need to be determined to complete the calculation.
Transcribed Image Text:**Graph Description:** The image features a graph with the function \( y = f(x) \) represented by a red curve. There are five green rectangles under the curve along the x-axis, ranging from \( x = 0 \) to \( x = 4 \). These rectangles illustrate a midpoint approximation for estimating the area under the curve. Each rectangle's height corresponds to the value of the function at the midpoint of its base. **Equation Instructions:** 5. The five rectangles shown represent a midpoint approximation for the area under the curve, \( y = f(x) \). Complete the equation, by writing the formula for the sum of the areas of the rectangles: \[ A \approx \text{Area 1} + \text{Area 2} + \text{Area 3} + \text{Area 4} + \text{Area 5} \] \[ A \approx ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) + ( \ ) \ast f( \ ) \] The rectangles' base widths and function evaluation points at each midpoint need to be determined to complete the calculation.
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