# How do you find the average value of #f(x)=2^x# as x varies between #[1,4]#?

##### 1 Answer

Mar 30, 2017

#### Explanation:

The formula for average value of a continuous function

Our formula here will be

#A = 1/(4 - 1) int_1^4 2^x dx#

#A = 1/3 int_1^4 2^x dx#

#A = 1/3[2^x/ln2]_1^4#

#A = 1/3[2^4/ln2 - 2^1/ln2]#

#A = 1/3[14/ln2]#

#A = 14/(3ln2)#

This can be approximated as

Hopefully this helps!