I'm stuck on a problem that deals with arc length. I know how to calculate the arc length in general, but I seem to have forgotten what to do in this particular situation. I know it's simple, but my book barely explains it, and I have failed to find any information online. Any help would be great!
$$ y =\int_1^x\sqrt{t^2-1} \ dt \ , 4\leq x \leq 7 $$
Answer = $$33/2$$
If someone could point me in the right direction on how to solve this, I would be thrilled!
We need to find $$\int_4^7\sqrt{1+\left(\frac{dy}{dx}\right)^2}\,dx.$$
By the Fundamental Theorem of Calculus, $\frac{dy}{dx}=\sqrt{x^2-1}$.
Square, add $1$, take the square root. We end up with something quite simple.