What is f(x) = int (x-4)^3 dx if f(3)=-1 ?
1 Answer
Mar 17, 2016
Explanation:
To integrate, use substitution, then use the rule
intu^ndu=u^(n+1)/(n+1)+C
If we set
f(x)=intu^3du
Applying the rule, this becomes
f(x)=u^4/4+C
f(x)=(x-4)^4/4+C
Now, we can determine
-1=(3-4)^4/4+C
=-1=(-1)^4/4+C
=-1=1/4+C
-5/4=C
So,
f(x)=(x-4)^4/4-5/4=((x-4)^4-5)/4