Answer :
Final answer:
To evaluate the integral ∫₉¹³ f(x) dx with the average value of f(x) over the interval [9,13] as 193, we can use the fact that the average value is equal to the integral divided by the length of the interval. By rearranging the equation and solving for the integral, we find that the value of the integral ∫₉¹³ f(x) dx is 772.
Explanation:
To evaluate the integral ∫₉¹³ f(x) dx, we can use the fact that the average value of f(x) over the interval [9,13] is 193. The average value of a function over an interval is equal to the integral of the function over that interval divided by the length of the interval.
So, we have:
193 = (∫₉¹³ f(x) dx) / (13 - 9)
193 = (∫₉¹³ f(x) dx) / 4
Multiplying both sides by 4 gives us:
772 = ∫₉¹³ f(x) dx
Therefore, the value of the integral ∫₉¹³ f(x) dx is 772. So, the answer is option b) 772.
