Answer :
Final Answer:
If the average value of f(t)=3t² + 6t - 83 over the interval [0, b] is 5. The value of b is 4.
Explanation:
To find the average value of a function f(t) over an interval [a, b], we use the formula:
Average value = (1/(b-a)) * ∫[a to b] f(t) dt
Given f(t) = 3t^2 + 6t - 83 and the average value is 5, we have:
(1/b) * ∫[0 to b] (3t^2 + 6t - 83) dt = 5
Integrating and solving for b, we get:
b^3 + 3b^2 - 88b = 0
b(b^2 + 3b - 88) = 0
Therefore, b = 4.
