What is f(x) = int (3x)/(x-4) if f(2)=1 ?
1 Answer
Explanation:
Integrating this is a little tricky:
First, bring out the constant
f(x)=3intx/(x-4)dx
From here, either long divide
=3int(x-4+4)/(x-4)dx=3int(x-4)/(x-4)+4/(x-4)dx
=3int1+4/(x-4)dx
Split up the integrals:
=3int1dx+3int4/(x-4)dx
Here, remember that the
=3x+3int4/(x-4)dx
Bring out the
=3x+12int1/(x-4)dx
Notice that we have an integral in the form
Since
f(x)=3x+12lnabs(x-4)+C
Now, we can use the original condition
1=3(2)+12lnabs(2-4)+C
1=6+12lnabs(-2)+C
-5=12ln2+C
-5-12ln2=C
Plug the value of
f(x)=3x+12lnabs(x-4)-5-12ln2