Question

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

Answer 1

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!