Find the average value of f(x)=6x+1 over [5,9]

Answer 1

The average value of f(x) over [5,9] is given by:

(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.