What is f(x) = int xsqrt(5-2) dx if f(2) = 3 ?

1 Answer
Apr 29, 2018

The function f(x) is (x^2sqrt3+6-4sqrt3)/2.

Explanation:

First, compute the integral:

f(x)=intxsqrt(5-2) dx

color(white)(f(x))=intxsqrt3 dx

color(white)(f(x))=sqrt3intx dx

Power rule:

color(white)(f(x))=sqrt3*x^2/2+C

Now, set f(2) (which is 3) and the integral evaluated at 2 equal to each other, then solve for C:

3=sqrt3*2^2/2+C

3=2sqrt3+C

3-2sqrt3=C

That's the C value, so that means that the function is:

f(x)=sqrt3*x^2/2+3-2sqrt3

If you would like, you can rewrite it as:

f(x)=(x^2sqrt3+6-4sqrt3)/2

Hope this helped!