How do I integrate this equation with respect to "x"? I am quite sure I need to use trigonometric substitution (or even hyperbolic), but I am not good at these methods since I just learned about trigonometric substitution. This is the equation of an ellipse. I know I have to re-write the equation so that it has an "integratable" form, but I struggle to work it out.
Is this the answer?
Or is this the answer?
Hint:
Factor out $a$, then $c$, to obtain $$\sqrt{a^2\biggl(c^2-\biggl(\frac{x-h}b\biggr)^{\!\!2\,}\biggr)}=|ac|\sqrt{1-\biggl(\frac{x-h}{bc}\biggr)^{\!\!2\,}}$$ and set $x-h=bc\sin u$, $\;\mathrm dx=bc\cos u\,\mathrm d u$.