### Inverse Functions

Inverse Functions The inverse of any function $displaystyle (f)$ is a function that will do the opposite of $displaystyle f$. In other words the function that will undo the effects of $displaystyle f$. So, if $displaystyle f$ maps 4 into 13, then the inverse of $displaystyle f$ will map 13 […]
Integration of a inverse Trigtonometric Forms We know the derivatives of the inverse trigonometric functions $displaystyle (text{arcsinx}{)}’=frac{1}{{sqrt{{1-{{x}^{2}}}}}}$ $displaystyle (text{arccosx}{)}’=frac{{-1}}{{sqrt{{1-{{x}^{2}}}}}}$ $displaystyle (arctgx{)}’=frac{1}{{1+{{x}^{2}}}}$ $displaystyle (text{arccotgx}{)}’=frac{{-1}}{{1+{{x}^{2}}}}$ $displaystyle (text{arcsecx}{)}’=frac{1}{{left| x right|sqrt{{{{x}^{2}}-1}}}}$ $displaystyle (text{arccscx}{)}’=frac{{-1}}{{left| x right|sqrt{{{{x}^{2}}-1}}}}$ Using those derivatives above, we can obtain the integrals as below, where u is a function of x that u=f(x). $displaystyle int{{frac{{du}}{{sqrt{{{{a}^{2}}-{{u}^{2}}}}}}}}=arcsin frac{u}{a}+C$ $displaystyle int{{frac{{du}}{{{{a}^{2}}+{{u}^{2}}}}}}=frac{1}{a}arctan frac{u}{a}+C$ \$displaystyle […]