Notice that the graph of f(x) is a downward-opening parabola with vertex at (0, 9) and x-intercepts at (-3, 0) and (3, 0). So the graph of f(x) ---Select--- ✓ lie on or above the x-axis over the interval [1, 3]. To approximate the area under the curve, we use the areas of rectangles whose bases are on the x-axis and whose heights are the vertical distances from points on their bases to the curve. We divide the interval [1, 3] into n = 4 equal subintervals and use them as the bases of n rectangles whose heights are determined by the curve. (See the figure below.) 10 y −1 8 4 2 1 2 Notice that the figure shows that using left-endpoints will give an approximation that ---Select--- The width of each of these rectangles is the result of dividing the length of the interval [1, 3] by n = 4. Determine the width of each rectangle. the length of the interval width = = = 31 4 n the true area.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
Question
Notice that the graph of f(x) is a downward-opening parabola with vertex at (0, 9) and x-intercepts at (-3, 0) and (3, 0). So the graph of f(x) ---Select--- ✓ lie on or above the x-axis over the interval [1, 3].
To approximate the area under the curve, we use the areas of rectangles whose bases are on the x-axis and whose heights are the vertical distances from points on their bases to the curve.
We divide the interval [1, 3] into n = 4 equal subintervals and use them as the bases of n rectangles whose heights are determined by the curve. (See the figure below.)
10
y
−1
8
4
2
1
2
Notice that the figure shows that using left-endpoints will give an approximation that ---Select---
The width of each of these rectangles is the result of dividing the length of the interval [1, 3] by n = 4.
Determine the width of each rectangle.
the length of the interval
width
=
=
=
31
4
n
the true area.
Transcribed Image Text:Notice that the graph of f(x) is a downward-opening parabola with vertex at (0, 9) and x-intercepts at (-3, 0) and (3, 0). So the graph of f(x) ---Select--- ✓ lie on or above the x-axis over the interval [1, 3]. To approximate the area under the curve, we use the areas of rectangles whose bases are on the x-axis and whose heights are the vertical distances from points on their bases to the curve. We divide the interval [1, 3] into n = 4 equal subintervals and use them as the bases of n rectangles whose heights are determined by the curve. (See the figure below.) 10 y −1 8 4 2 1 2 Notice that the figure shows that using left-endpoints will give an approximation that ---Select--- The width of each of these rectangles is the result of dividing the length of the interval [1, 3] by n = 4. Determine the width of each rectangle. the length of the interval width = = = 31 4 n the true area.
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