Question 1. Graphical Integration Challenge: u-Substitution and Integration by Parts Let F(x) = = G(x) = f*g(t) f(t) dt and G(z) y = f(x) 2 g(t) dt, where the graphs of f(x) and g(x) on [-2, 4] are below. 7 2 1 2 3 y = g(x) (a) Evaluate [F(x)f(x) = G(x)g(x)] dr. 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(1))G(x)g(2) dz. 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)=1xf(t)dt and G(x)=0xg(t)dt, where the graphs of f(x) and g(x) on 2,4 are below. (a) Evaluate 02[F(x)f(x)G(x)g(x)]dx HINT: Consider a u-substitution (possibly multiple substitutions). You may need to invoke Part I of the Fundamental Theorem of Calculus. (b) Evaluate 01f(G(x))G(x)g(x)dx 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)=1xf(t)dt and G(x)=0xg(t)dt, where the graphs of f(x) and g(x) on 2,4 are below. (a) Evaluate 02[F(x)f(x)G(x)g(x)]dx HINT: Consider a u-substitution (possibly multiple substitutions). You may need to invoke Part I of the Fundamental Theorem of Calculus. (b) Evaluate 01f(G(x))G(x)g(x)dx HINT: Consider a u-substitution. You may also need to integrate by parts