Thread: find the average value of the function - with an e

Hi

The goal is to find the average value of the function h (t) = 1/(e^2t) over the interval (0,1)

So havg (1-0) = S a=0; b=1 e^-2t dt

So I am assuming I should do some substitution

let u = e^-2t then du =-2e^-2t dt so du/-2 = e^-2t dt

Then havg = S a=0;b=1 du/-2 = -1/2 S du = -1/2 (u) a=0;b=1

So then -1/2 (e^-2t) a=0;b=1

= -1/2 (e^-2 - e^0)

= -1/(2e) + 1

Did I do this correctly???

Thanks

Calculus beginner - who no longer likes the letter e

Originally Posted by calcbeg

Hi

The goal is to find the average value of the function h (t) = 1/(e^2t) over the interval (0,1)

So havg (1-0) = S a=0; b=1 e^-2t dt

So I am assuming I should do some substitution

let u = e^-2t then du =-2e^-2t dt so du/-2 = e^-2t dt

Then havg = S a=0;b=1 du/-2 = -1/2 S du = -1/2 (u) a=0;b=1

So then -1/2 (e^-2t) a=0;b=1

= -1/2 (e^-2 - e^0) So far, so good

= -1/(2e) + 1 you simplified incorrectly

Did I do this correctly???

Thanks

Calculus beginner - who no longer likes the letter e

And is great:

Learn to love it, because it never goes away.