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0471433314realan... x 玩, 早2 &D EEEO 216 (232 of 4S) 121% exist in R, or where it does not equal f(c). It turns out that we can permit a finite number of such exceptional points. 7.3.1 Fundamental Theorem of Calculus (First Form) Suppose there is a finite set E in [a, b] and functions f, F := [a,b] →R such that: (a) F is continuous on [a, b], (b) F'(x) =f(x) for all x E [a, b]\E, (c) f belongs to R[a,b]. Then we have (1) f = F(b) - F(a). %3D

0471433314realan... x 玩, 早2 &D EEEO 216 (232 of 4S) 121% exist in R, or where it does not equal f(c). It turns out that we can permit a finite number of such exceptional points. 7.3.1 Fundamental Theorem of Calculus (First Form) Suppose there is a finite set E in [a, b] and functions f, F := [a,b] →R such that: (a) F is continuous on [a, b], (b) F'(x) =f(x) for all x E [a, b]\E, (c) f belongs to R[a,b]. Then we have (1) f = F(b) - F(a). %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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Could i get a prove for this theorem using Reimann integral definition  when the points in the set E={C0,C1,C2,....,Cm} where F'(x) doesn't equal f(x)

0471433314realan... x 216 (232 of 4S) 121% exist in R, or where it does not equal f(c). It turns out that we can permit a finite number of such exceptional points. 7.3.1 Fundamental Theorem of Calculus (First Form) Suppose there is a finite set E in [a, b] and functions f, F := [a, b] → R such that: (a) F is continuous on [a, b], (b) F'(x) =f(x) for all x E [a, b] \E, (c) f belongs to R(a,b]. Then we have (1) f = F(b) – F(a).
Transcribed Image Text:0471433314realan... x 216 (232 of 4S) 121% exist in R, or where it does not equal f(c). It turns out that we can permit a finite number of such exceptional points. 7.3.1 Fundamental Theorem of Calculus (First Form) Suppose there is a finite set E in [a, b] and functions f, F := [a, b] → R such that: (a) F is continuous on [a, b], (b) F'(x) =f(x) for all x E [a, b] \E, (c) f belongs to R(a,b]. Then we have (1) f = F(b) – F(a).
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