Areas, Arc Length, Surface Area Consider the area between the graphs of f(x) = x² – 1 and g(x) = x from -2 < x < 4. • It would be incorrect to set up this integral as follows: | f(x) – 9(x) dx. Why? • That integral, f(x) – g(x) dx, does describe something – what does it describe? • Write an integral that finds the indicated area, and compute it. • Suppose we only want the area between f(x) and g(x) from 0 < x < 2. Set this up as an integral with respect to y. No need to solve this one.
Areas, Arc Length, Surface Area Consider the area between the graphs of f(x) = x² – 1 and g(x) = x from -2 < x < 4. • It would be incorrect to set up this integral as follows: | f(x) – 9(x) dx. Why? • That integral, f(x) – g(x) dx, does describe something – what does it describe? • Write an integral that finds the indicated area, and compute it. • Suppose we only want the area between f(x) and g(x) from 0 < x < 2. Set this up as an integral with respect to y. No need to solve this one.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Areas, Arc Length, Surface Area
Consider the area between the graphs of f(x) = x² – 1 and g(x) = x from -2 < x < 4.
• It would be incorrect to set up this integral as follows:
| f(x) – 9(x) dx. Why?
• That integral,
f(x) – g(x) dx, does describe something – what does it describe?
• Write an integral that finds the indicated area, and compute it.
• Suppose we only want the area between f(x) and g(x) from 0 < x < 2. Set this up as an integral with
respect to y. No need to solve this one.
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