What is f(x) = int 1/(sqrt(x+3) if f(2)=1 ?

1 Answer
Jan 25, 2016

f(x) = 2sqrt(x+3)+1-2sqrt(5)

Explanation:

First, we evaluate the indefinite integral using u substitution.

Let u = x+3 => du = dx

Then

int1/sqrt(x+3)dx = int1/sqrt(u)du

=intu^(-1/2)du

=u^(1/2)/(1/2)+C

=2sqrt(x+3)+C

Now, we evaluate at x=2 to find the value of C

f(2) = 2sqrt(2+3)+C = 1

=> C = 1-2sqrt(5)

Thus, we have

f(x) = 2sqrt(x+3)+1-2sqrt(5)