Given $f(x,y,z) = \sqrt{1+4x^2z^2}$. How do I calculate the line integral along the intersection between $x^2+z^2 = 1$ and $y=x^2$? I found this parametrization:
$\vec{r} : t \rightarrow (t, t^2, \sqrt{1-t^2})$, with $a <t <b$, but I don't know how to find $a$ and $b$.
I tried using $\int_a^b f(\vec{r}(t)) \| \frac{dr}{dt} \| dt$, but I couldn't solve it using that formula.