# Use a table of integrals to evaluate the following integrals. int (dy)/(sqrt(4-y^(2)))

Use a table of integrals to evaluate the following integrals. $\int \frac{dy}{\sqrt{4-{y}^{2}}}$
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$\int \frac{dy}{\sqrt{4-{y}^{2}}}$
Rewrite
$\int \frac{dy}{\sqrt{4-{y}^{2}}}=\int \frac{dy}{\sqrt{\left(2{\right)}^{2}-{y}^{2}}}$
Formula: $\int \frac{du}{\sqrt{{a}^{2}-{u}^{2}}}={\mathrm{sin}}^{-1}\left(\frac{u}{a}\right)+C$
Let a=2 and u=y
Therefore,
$\int \frac{dy}{\sqrt{\left(2{\right)}^{2}-{y}^{2}}}={\mathrm{sin}}^{-1}\left(\frac{y}{2}\right)+C$
Simplify
$\int \frac{dy}{\sqrt{4-{y}^{2}}}={\mathrm{sin}}^{-1}\left(\frac{y}{2}\right)+C$