## Calculus 10th Edition

$\int_0^7\frac{1}{\sqrt {100-x^{2}}}dx=arcsin\frac{7}{10}$
$\int_0^7\frac{1}{\sqrt {100-x^{2}}}dx$ $=\int_0^7\frac{1}{\sqrt {(10)^{2}-x^{2}}}dx$ Use arcsine formula: $arcsin\frac{u}{a}+C=\int \frac{1}{\sqrt {a^{2}-u^{2}}}du$ $=arcsin\frac{x}{10}|_0^7$ $=arcsin\frac{7}{10}-arcsin0$ $=arcsin\frac{7}{10}-0$ $=arcsin\frac{7}{10}$