Further Maths - Integrating and Differentiating Inverse Trig Functions
See Also
- [[Further Maths - Mean Value of a Function]]A
- [[Further Maths - Improper Integrals]]A
- [[Further Maths - Hyperbolic Functions]]A
Flashcards
#####
\[\frac{d}{dx}(\sin^{-1}(x))\]What is this equal to??
\[\frac{1}{\sqrt{1 - x^2}}\]#####
\[\frac{d}{dx}(\cos^{-1}(x))\]What is this equal to??
\[-\frac{1}{\sqrt{1 - x^2}}\]#####
\[\frac{d}{dx}(\tan^{-1}(x))\]What is this equal to??
\[\frac{1}{1 + x^2}\]#####
\[\int \frac{1}{\sqrt{1-x^2}} dx\]What is this equal to??
\[\sin^{-1}(x) + c\]#####
\[\int -\frac{1}{\sqrt{1-x^2}} dx\]What is this equal to??
\[\cos^{-1}(x) + c\]#####
\[\int \frac{1}{1 + x^2}dx\]What is this equal to??
\[\tan^{-1}(x) + c\]#####
\[\int \frac{1}{\sqrt{a^2-x^2}} dx\]What is this equal to??
\[\sin^{-1}\left(\frac{x}{a}\right) + c\]#####
\[\int \frac{1}{a^2 + x^2}dx\]What is this equal to??
\[\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right) + c\]