Find the average of f(x)=sqrt(1-x) on the interval [-1,1]?

[Chandasouk]

Please show work. There was a negative sign that appeared in the solution and I don't know why.

I know $$\sqrt{}(1-X)$$ can be rewritten as (1-X)^1/2 and then you use the power rule to integrate but that gives you

(1-x)^3/2
------------
3/2

2(1-X)^3/2
--------------
3

My book shows

-(1-X)^3/2
------------
3/2

instead

 

[Dick]

You integrate that by using the substitution u=1-x. So dx=(-du). Then use the power rule on the u integral. That's where the '-' sign comes from.