Question

Find the average value of the function over the given interval.

(Round your answer to three decimal places.)
f(x) = cos(x), [0, pie/6]
Find all values of x in the interval for which the
function eqution

Answer 1

The average value of the function f(x) = cos(x) over the interval [0, pi/6] is 0.5.

Step-by-step explanation:

To find the average value of the function f(x) = cos(x) over the interval [0, pi/6], we first need to evaluate the function at multiple points within the interval and then find the average of those values.

The function f(x) = cos(x) can be evaluated at the following points within the interval [0, pi/6]:

f(0) = cos(0) = 1 f(π/6) = cos(π/6) = 1/2

To find the average value of the function over the interval, we can use the formula:

average = (f(0) + f(π/6)) / 2

Substituting the values, we get:

average = (1 + 1/2) / 2 = 0.5

Therefore, the average value of the function f(x) = cos(x) over the interval [0, pi/6] is 0.5.