I am a high school calculus teacher. I’m working through some review problems that I’m about to give my students and I’m stumped by one of them.
If F’(x)=sqrt(1+x^3) and F(1) = 5, then F(3) = ?
The answer is 11.230 but I can’t figure out how to get there.
My initial thought was to find the integral of F’(x) to get F(x), use F(1) = 5 to solve for C, then evaluate the new function for F(3). But this technique falls apart since you can’t integrate sqrt(1+x^3) directly without x^2 on the outside.