The average value of a function f(x) over an interval [a,b] is given by the formula: Average =
1
b−a
b
∫
a
f(x)dx In this case, we want to find the average value of the function y=sin(x) over the interval [0,π]. We can use the formula above, with f(x)=sin(x),a=0, and b=π : Average =
1
π−0
π
∫
0
sin(x)dx The integral of sin(x) from 0 to π is −cos(π)+cos(0)=−(−1)+1=2. So, the average value is : Average =