# Thread: fundamental theorem!!!

1. ## fundamental theorem!!!

Use the figure below to find the following quantities.

(a)

(b) The average value of f(x) on the interval [1, 6].

can i get some help with this bad flippin johnny, thanks...

mathlete

2. (a) What does a definite integral mean? Surely you know it's the area under the curve. You know each square is $1 units^{2}$ in area so you can figure out what the area under the curve is.

(b) Average value of a function over an interval [a,b] is given by:
$f_{avg} = \frac{1}{b-a} {\color{blue} \int_{a}^{b} f(x) dx}$

You are given a and b and you know found the definite integral from (a).

3. Originally Posted by mathlete
Use the figure below to find the following quantities.

(a)

(b) The average value of f(x) on the interval [1, 6].

can i get some help with this bad flippin johnny, thanks...

mathlete
The integral is just the total area under the curve between 1 and 6. Area equals 8.5 if you count up the blocks.

Average value is simply the area divided by the range or $\frac{8.5}{5} = \frac{17}{10} \Rightarrow 1.7$