Primitive of Reciprocal of Root of a squared minus x squared/Examples/16 - x^2

Example of Use of Primitive of $\dfrac 1 {\sqrt {a^2 - x^2} }$

$\ds \int \dfrac 1 {\sqrt {16 - x^2} } \rd x = \arcsin \dfrac x 4 + C$

Proof

From Primitive of $\dfrac 1 {\sqrt {a^2 - x^2} }$:

$\ds \int \frac {\d x} {\sqrt {a^2 - x^2} } = \arcsin \frac x a + C$

The result follows by setting $a = 4$.

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XIV}$: $12$.