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Question 4 (9 points) Consider a continuous function f which is defined for all real numbers x and has the following properties: • ??³ f(x) dx = 5/2. • ??? f(x) dx = 10. (a) (3 points) Find the average value of f on the interval [1, 3]. (b) (3 points) Find the value of ??? (2f(x) - 3) dx. (c) (3 points) Now suppose f is linear, i.e. f(x) = ax + b. Find the constants a and b.

          Question 4 (9 points) Consider a continuous function f which is defined for all real numbers x and has the following properties:
• ??³ f(x) dx = 5/2.
• ??? f(x) dx = 10.
(a) (3 points) Find the average value of f on the interval [1, 3].
(b) (3 points) Find the value of ??? (2f(x) - 3) dx.
(c) (3 points) Now suppose f is linear, i.e. f(x) = ax + b. Find the constants a and b.

Question 4 (9 points) Consider a continuous function f which is defined for all real numbers x and has the following properties:
• ??³ f(x) dx = 5/2.
• ??? f(x) dx = 10.
(a) (3 points) Find the average value of f on the interval [1, 3].
(b) (3 points) Find the value of ??? (2f(x) - 3) dx.
(c) (3 points) Now suppose f is linear, i.e. f(x) = ax + b. Find the constants a and b.

Added by Angela C.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

07/18/2023

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Question 4 (9 points) Consider a continuous function f which is defined for all real numbers x and has the following properties: • ∫₁³ f(x) dx = 5/2. • ∫₁⁵ f(x) dx = 10. (a) (3 points) Find the average value of f on the interval [1, 3]. (b) (3 points) Find the value of ∫₃⁵ (2f(x) - 3) dx. (c) (3 points) Now suppose f is linear, i.e. f(x) = ax + b. Find the constants a and b.