Primitive of Root of a squared minus x squared/Arcsine Form/Mistake

Source Work

2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.):

Appendix $7$: Integrals

Mistake

$\ds \int \sqrt {x^2 + x^2} \rd x = \frac 1 2 x \sqrt {x^2 + x^2} + \frac 1 2 a^2 \sin^{-1} \frac x a$

Correction

This should read:

$\ds \int \sqrt {a^2 - x^2} \rd x = \frac 1 2 x \sqrt {a^2 - x^2} + \frac 1 2 a^2 \sin^{-1} \frac x a$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous): Appendix $7$: Integrals