What is f(x) = int x/sqrt(x^2+1) dx if f(2) = 3 ?
1 Answer
Mar 20, 2016
Explanation:
To integrate:
Let
This gives us:
f(x)=1/2int(2x)/sqrt(x^2+1)dx=1/2int1/sqrtudu=1/2intu^(-1/2)du
Now, we integrate using the rule:
So, we have
f(x)=1/2u^(1/2)/(1/2)+C=1/2sqrtu*2+C=sqrtu+C
f(x)=sqrt(x^2+1)+C
Using the original condition
3=sqrt(2^2+1)+C
3=sqrt5+C
C=3-sqrt5
So, substituting this in, we see that
f(x)=sqrt(x^2+1)+3-sqrt5