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The Fundamental Theorem of Calculus, Part 1: If f is continuous on [a,b], then the function g defined by 9 (x) = S. f (t) dt, a < a < b %D is continuous on [a,b], and differentiable on (a,b), and d (x) = f (x). %3D

The Fundamental Theorem of Calculus, Part 1: If f is continuous on [a,b], then the function g defined by 9 (x) = S. f (t) dt, a < a < b %D is continuous on [a,b], and differentiable on (a,b), and d (x) = f (x). %3D

Advanced Engineering Mathematics
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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The Fundamental Theorem of Calculus, Part 1: If f is continuous on [a,b], then the function g defined by g(x)%3D S" f (t) dt, a < x < b is continuous on [a,b], and differentiable on (a,b), and d (x) = f (x).
Transcribed Image Text:The Fundamental Theorem of Calculus, Part 1: If f is continuous on [a,b], then the function g defined by g(x)%3D S" f (t) dt, a < x < b is continuous on [a,b], and differentiable on (a,b), and d (x) = f (x).
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