if the average value of f(x) on the interval 2≤ x ≤ 7 is 9, find ∫72 (4f(x)+2)dx = what

Question

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if the average value of f(x) on the interval 2≤ x ≤ 7 is 9, find ∫ (4f(x)+2)dx = what

Answer 1

[1/(7-2)] ∫f(x)dx = 9 So, ∫f(x)dx = 45

Therefore, ∫_{(from 2 to 7)} [4f(x) + 2]dx = 4 ∫_{(from 2 to 7)}f(x)dx + ∫_{(from 2 to 7)}2dx = 4(45) + 10 = 190