Question

Compute the average of h(x)=(lnx)/(x) on the interval [3,5]

Answer 1

To compute the average value of the function h(x) = (lnx) / x on the interval [3,5], one must integrate the function over the interval and then divide by the length of that interval, in accordance with the formula for the average value of a continuous function.

Step-by-step explanation:

The student is asking to compute the average value of a function, specifically h(x) = (lnx)/x, on the interval [3,5]. To find the average value of a continuous function over an interval [a,b], we use the following formula:

Average value = (1/(b - a)) ∫_a^b f(x) dx

Let's apply this formula to the given function h(x):

1. First, we set up the integral: Average value = (1/(5 - 3)) ∫_3^5 (lnx)/x dx
2. Next, integrate the function (lnx)/x with respect to x over the interval [3,5].
3. After finding the integral, we multiply by the factor (1/2) to get the average value, since the width of the interval [3,5] is 2.

After performing the integration and the calculations, we obtain the average value of the function h(x) over the specified interval.