What is #f(x) = int x^2+x-3# if #f(2)=3 #?

1 Answer
Mar 3, 2016

Answer:

I found: #f(x)=x^3/3+x^2/2-3x+13/3#

Explanation:

We solve the indefinite integral:
#int(x^2+x-3)dx=x^3/3+x^2/2-3x+c#
and then we use our condition to find #c#:
#f(2)=3=(2^3)/3+(2^2)/2-(3*2)+c#
so:
#3=8/3+4/2-6+c#
#c=3-8/3-2+6#
#c=7-8/3=(21-8)/3=13/3#
and finaly:
#f(x)=x^3/3+x^2/2-3x+13/3#