How do you use the integral fomula to find the average value of the function #f(x)=18x# over the interval between 0 and 4?

1 Answer
Aug 12, 2015

I found: #y_(av)=36#

Explanation:

Consider a general case:
enter image source here
The average value of your function #y_(av)# will be the one that makes the area 1 exactly equal to area 2: So the area under the curve will be exactly the area of the rectangular region (blue+area 1).
The rectangular area #A# will be:
#A=basexxheight=(x_2-x_1)*y_(av)=int_(x_1)^(x_2)f(x)dx#
and so:
#color(red)(y_(av)=1/(x_2-x_1)*int_(x_1)^(x_2)f(x)dx)#

In your case:
#y_(av)=1/(4-0)*int_(0)^(4)18xdx=18/4[x^2/2]_0^4#

so finally:

#y_(av)=36#

Graphically:
enter image source here