Over what open interval does the formula F(x)=[int (from 1 to x) dt/t]
represent an antiderivative of f(x)=1/x? and find a point where the graph of F crosses the x-axis.
I don't even how to start calculating this problem.
Thank you
hmm, since you are already in the integrals, you should already know the function for which you differentiate it gives $\displaystyle \frac{1}{x}$.
let $\displaystyle F(x) = \ln x$. Then $\displaystyle F'(x) = \frac{1}{x}$.
Thus, by FTOC, $\displaystyle F(x) = \int_a^x \frac{1}{t} \, dt$, where $\displaystyle a>0$..