Calculate he average over the given interval: f(x)=e^(-n*x), [-1,1].

Question

I know that the average value = (1/b-a)integrate from a to b f(x)dx

Answer 1

You have stated the definition of the average value correctly. All you have to do is perform the integration and divide the integral by the integration interval, 2.

The indefinite integral of e^(-nx) is (-1/n)*e^(-nx).

The definite integral from -1 to 1 is
(-1/n)[e^-n - e^n]

Divide that by 2 for the average value.

Check my math. I am often sloppy.

Answer 2

thanks, but can we leave it in that form?

Answer 3

You can convert my answer to a hyperbolic sine of n, divided by 2, if you wish.

Answer 4

I meant "divided by n", not 2

Answer 5

What is hyperbolic sin of n? Never heard of that.