Find the average rate of change of f of x equals 1 + sin x over the interval [0, pi/2]?

For every change in x, y changes 2/pi.

In order to find this we first need to evaluate the expression at the intervals.

x = 0

f(x) = 1 + sinx

f(0) = 1 + sin0

f(0) = 1 + 0

f(0) = 0

x = pi/2

f(x) = 1 + sinx

f(pi/2) = 1 + sin(pi/2)

f(pi/2) = 1 + 1

f(pi/2) = 2

So the total change in y is 1. So we divide that by how much x has changed in that interval to find the average rate of change.

1 / (pi/2) = 2/pi