Question

How do you find the average value of the function for `f(x)=1-x^4, -1<=x<=1`?

Answer 1

The average value is `4/5`.

Explanation:

The average value is given by

`A = 1/(b - a) int_a^b f(x)dx`

Where `f(x)` is a continuous function on `[a, b]`.

`A = 1/(1 - (-1)) int 1 - x^4`

`A = 1/2[(x - 1/5x^5)]_-1^1`

`A = 1/2(1 - 1/5 - (-1 - 1/5(-1)^5))`

`A = 1/2(4/5 + 1 - 1/5)`

`A = 1/2(8/5)`

`A = 4/5`

Hopefully this helps!