What is #f(x) = int e^(3x)-e^(x)dx# if #f(0)=-2 #?

1 Answer
Gió
May 16, 2016

I found: #f(x)=e^(3x)/3-e^x-4/3#

Explanation:

We can solve the integral and write:
#f(x)=inte^(3x)dx-inte^xdx=e^(3x)/3-e^x+c#
now we need to find #c#;
we use the fact that #f(0)=-2#, i.e., we use #x=0# and set it equal to #-2#:
#e^(3*0)/3-e^0+c=-2#
#1/3-1+c=-2#
#c=1-2-1/3=-4/3#
giving your final function as:
#f(x)=e^(3x)/3-e^x-4/3#

Related questions
See all questions in Evaluating the Constant of Integration
Impact of this question
1256 views around the world
You can reuse this answer
Creative Commons License