Find the arc-length of a circle with radius a.
From the equation of a circle, I found out the equation for the one quadrant, which is:
$y = \sqrt{a^2 - x^2}$
I tried solving the problem, and here's what I did:
$$A = 4 \int_0^a \sqrt{1+\frac{x^2}{a^2-x^2}}dx$$
$$A = 4 \int_0^a \frac{a}{\sqrt{{a^2-x^2}}}dx $$
And this is where I need help. How can solve this integral now?
2026-04-24 07:44:24.1777016664
Find the arc-length of the circle with radius a?
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Hint: Fix the problem, it should be $y = \sqrt{a^2 - x^2}$ as i edited it. Then use the substitution $x=a\sin \theta$