(avg value) = (1/(9-5)) * ∫(5 to 9) f(x) dx = (1/4) * ∫(5 to 9) (6x+1) dx = (1/4) * [3x^2 + x] from 5 to 9 = (1/4) * [(3*9^2 + 9) - (3*5^2 + 5)] = (1/4) * [243+9 - 125-5] = (1/4) * 122 = 30.5 Therefore, the average value of f(x)=6x+1 over [5,9] is 30.5.
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