What is f(x) = int x^2+x-3f(x)=∫x2+x−3 if f(2)=3 f(2)=3?

1 Answer
Gió
Mar 3, 2016

I found: f(x)=x^3/3+x^2/2-3x+13/3f(x)=x33+x22−3x+133

Explanation:

We solve the indefinite integral:
int(x^2+x-3)dx=x^3/3+x^2/2-3x+c∫(x2+x−3)dx=x33+x22−3x+c
and then we use our condition to find cc:
f(2)=3=(2^3)/3+(2^2)/2-(3*2)+cf(2)=3=233+222−(3⋅2)+c
so:
3=8/3+4/2-6+c3=83+42−6+c
c=3-8/3-2+6c=3−83−2+6
c=7-8/3=(21-8)/3=13/3c=7−83=21−83=133
and finaly:
f(x)=x^3/3+x^2/2-3x+13/3f(x)=x33+x22−3x+133

Related questions
See all questions in Evaluating the Constant of Integration
Impact of this question
4185 views around the world
You can reuse this answer
Creative Commons License