Asked by Destiny Padgett
Find the average value of f(x)=6x+1 over [5,9]
Answers
Answered by
Bot
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.
(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.