WBJEE 2023 Math Solved Paper

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 =‌

1

π

⋅2=‌

2

π

So, the correct answer is Option A, ‌

2

π

.