# Thread: Average Value of a Number

1. ## Average Value of a Number

Can someone please help me out with this problem? It is the last one I have for my calculus assignment due tomorrow! We haven't done anything like this in class, so I have NO idea what to do.

Here is a link to a picture of the problem because I couldn't type it on here.

http://img3.imageshack.us/img3/5082/mathfp5.jpg

2. Originally Posted by JollyJolly15
Can someone please help me out with this problem? It is the last one I have for my calculus assignment due tomorrow! We haven't done anything like this in class, so I have NO idea what to do.

Here is a link to a picture of the problem because I couldn't type it on here.

http://img3.imageshack.us/img3/5082/mathfp5.jpg

The average value of a Riemann-integrable functuon $\displaystyle f(x)$ over an interval $\displaystyle (a,b)\,,\,a<b$ is given by $\displaystyle \frac{1}{b-a}\int\limits^b_af(x)\,dx$

In your case, note that $\displaystyle \sec^2x=(\tan x)'$ , so the integral of that function is pretty easy...

Tonio

3. ## simple

we should do differentiation or integration??
if its deferenciation then
use the product principle rule
e^3tanx+1 * d/dx sec^2x + sec^2x * d/dx e^3tanx+1
= e^3tanx+1 * 2secx(secxtanx) + sec^2x * e^3tanx+1(3sec^2x)
then simplyfy it and substitute x as 0 and x as 45 and then add the values and divide them by 2,
you will get the answer

4. Originally Posted by grgrsanjay
we should do differentiation or integration??
if its deferenciation then
use the product principle rule
e^3tanx+1 * d/dx sec^2x + sec^2x * d/dx e^3tanx+1
= e^3tanx+1 * 2secx(secxtanx) + sec^2x * e^3tanx+1(3sec^2x)
then simplyfy it and substitute x as 0 and x as 45 and then add the values and divide them by 2,
you will get the answer
Tonio had already said that it was an integration

If you needed to find the average of a finite list of numbers, you would add them all up and divide by the "number of numbers". With a continuous function that "adding" becomes integrating.