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Question 1. Graphical Integration Challenge: u-Substitution and Integration by Parts Let F(x) = f(t) dt and G(a) = g(t) dt, where the graphs of f(a) and g(z) on [-2, 4) are below. v=f(x) 2 2 v=g(z). Evaluate F(a)f(2) - G(a)g(2) dr. HINT: Consider a u-substitution (possibly multiple substitutions). You may need to invoke Part I of the Fundamental Theorem of Calculus.. (b) Evaluate eff'(G(z) G(z)g(z) dr. HINT: Consider a u-substitution. You may also need to integrate by parts.

Question 1. Graphical Integration Challenge: u-Substitution and Integration by Parts Let F(x) = f(t) dt and G(a) = g(t) dt, where the graphs of f(a) and g(z) on [-2, 4) are below. v=f(x) 2 2 v=g(z). Evaluate F(a)f(2) - G(a)g(2) dr. HINT: Consider a u-substitution (possibly multiple substitutions). You may need to invoke Part I of the Fundamental Theorem of Calculus.. (b) Evaluate eff'(G(z) G(z)g(z) dr. HINT: Consider a u-substitution. You may also need to integrate by parts.

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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Question 1. Graphical Integration Challenge: u-Substitution and Integration by Parts Let F(x) = f(t) dt and G(z) = g(t) dt, where the graphs of f(a) and g(z) on [-2,4) are below. v=f(x) (a) 2 v=g(x) Evaluate F(x)f(x)=G(z)g(2) dz. HINT: Consider a u-substitution (possibly multiple substitutions). You may need to invoke Part I of the Fundamental Theorem of Calculus. (b) Evaluate. f'(G(z))G(r)g(r) dr. HINT: Consider a u-substitution. You may also need to integrate by parts.
Transcribed Image Text:Question 1. Graphical Integration Challenge: u-Substitution and Integration by Parts Let F(x) = f(t) dt and G(z) = g(t) dt, where the graphs of f(a) and g(z) on [-2,4) are below. v=f(x) (a) 2 v=g(x) Evaluate F(x)f(x)=G(z)g(2) dz. HINT: Consider a u-substitution (possibly multiple substitutions). You may need to invoke Part I of the Fundamental Theorem of Calculus. (b) Evaluate. f'(G(z))G(r)g(r) dr. HINT: Consider a u-substitution. You may also need to integrate by parts.
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