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To approximate the area under the curve in Figure 1, we can use rectangles as illustrated in Figures 2 and 3. For 4 rectangles, the approximating area is For 10 rectangles, the approximating area is For 100 rectangles, the approximating area is For 1000 rectangles, the approximating area is

To approximate the area under the curve in Figure 1, we can use rectangles as illustrated in Figures 2 and 3. For 4 rectangles, the approximating area is For 10 rectangles, the approximating area is For 100 rectangles, the approximating area is For 1000 rectangles, the approximating area is

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Value: 16 To approximate the area under the curve in Figure 1, we can use rectangles as illustrated in Figures 2 and 3. For 4 rectangles, the approximating area is For 10 rectangles, the approximating area is the Are For 100 rectangles, the approximating area is are For 1000 rectangles, the approximating area is As the number of rectangles gets larger and larger, the approximations get better and better. In fact, the limit of an infinite number of infinitesimally thin rectangles gives us the precise area under the curve in Figure 1, which is 26
Transcribed Image Text:Value: 16 To approximate the area under the curve in Figure 1, we can use rectangles as illustrated in Figures 2 and 3. For 4 rectangles, the approximating area is For 10 rectangles, the approximating area is the Are For 100 rectangles, the approximating area is are For 1000 rectangles, the approximating area is As the number of rectangles gets larger and larger, the approximations get better and better. In fact, the limit of an infinite number of infinitesimally thin rectangles gives us the precise area under the curve in Figure 1, which is 26
FIGURE 1 y = x (1, 1) of the region S tha FIGURE 2 y = x ra curve, we can sur (1, 1) thinner, the approxin e number of infinitesi V4 Va /41 FIGURE 3 y = x? On=8 (1, 1) Understanding Inte ntegration? Finding the Are (1, 1) are fr nun rec FIGURE 4 f(x) puTube
Transcribed Image Text:FIGURE 1 y = x (1, 1) of the region S tha FIGURE 2 y = x ra curve, we can sur (1, 1) thinner, the approxin e number of infinitesi V4 Va /41 FIGURE 3 y = x? On=8 (1, 1) Understanding Inte ntegration? Finding the Are (1, 1) are fr nun rec FIGURE 4 f(x) puTube
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