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