Find the average value of the function f over the indicated interval [0, 8].
f(x) = 7/(x + 1)
I keep getting the wrong answer.
To find the average value of a function over an interval [a, b], you need to compute the definite integral of the function over that interval, and then divide that result by the width of the interval (b - a).
In this case, you have the function f(x) = 7/(x + 1) and you want to find the average value over the interval [0, 8].
First, let's compute the definite integral of f(x) over the interval [0, 8]. We can do this by finding the antiderivative of f(x) and evaluating it at the upper and lower limits of integration:
∫(from 0 to 8) 7/(x + 1) dx = [7 ln(abs(x + 1))] (from 0 to 8)
= 7 ln(9) - 7 ln(1)
Now, let's find the width of the interval:
Width = b - a = 8 - 0 = 8
To find the average value, divide the definite integral by the width of the interval:
Average value = (7 ln(9) - 7 ln(1)) / 8
Now you can evaluate this expression to get the average value.