TheSimpliFire
My WordPress blog is here!
About: Where I store any mathematical problems I've made up :)
My favourite questions:
Finding the turning points of $f(x)=\left(x-a+\frac1{ax}\right)^a-\left(\frac1x-\frac1a+ax\right)^x$
Mathematical coincidences concerning the numbers $\pi$, $e$ and $163$
Convergence concerning the $\alpha$th derivative of $f(x)=x^{\alpha}-\alpha^x$
My favourite answers:
Evaluating $\int_0^1\frac{3x^4+ 4x^3 + 3x^2}{(4x^3 + 3x^2 + 2x+ 1)^2}\, dx$
How to prove :$\sqrt{1!\sqrt{2!\sqrt{3!\sqrt{\cdots\sqrt{n!}}}}} <3$
Evaluate $\int (1-x^{2008})^{\frac{1}{2007}} (1-x^{2007})^{\frac{1}{2008}} dx$
Just discovered a neat closed form of the following integral using $1$s and $2$s: $$\begin{align}\int_{\pi/8}^{\pi/4}\frac{\sin x+\cos x}{\tan x}\,dx&=\sqrt2-\frac{\sqrt{\sqrt2-1}+\sqrt{\sqrt2+1}}{\sqrt{2\sqrt2}}\\&\,\,\,\,\,\,+\ln\left(1+\sqrt2\sqrt{2-\sqrt2}\right)\end{align}$$
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- mathscmp.wordpress.com
- Member for 1 year
- 70 profile views
- Last seen 21 hours ago
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