6. Prove the following version of the Fundamental Theorem of Calculus: Theorem 1. Let F [a, b] → R be differentiable and suppose that F" : [a,b]→ R is Riemann integrable. Then [F F'(x) dx F(b) - F(a).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
icon
Related questions
Question
6. Prove the following version of the Fundamental Theorem of Calculus:
Theorem 1. Let F [a,b] → R be differentiable and suppose that F' :
[a, b] R is Riemann integrable. Then
[*F¹(x) dx
a
=
F(b)
F(a).
Transcribed Image Text:6. Prove the following version of the Fundamental Theorem of Calculus: Theorem 1. Let F [a,b] → R be differentiable and suppose that F' : [a, b] R is Riemann integrable. Then [*F¹(x) dx a = F(b) F(a).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage