## Problem of the Day #314: $\pi$January 27, 2012

Posted by Albert in : potd , add a comment

Saketh graphs $f(x) = \frac{1}{1+x^2}$ for $x \in [0,1]$. He cuts out the square $0 \leq x \leq 1$, $0 \leq y \leq 1$, then cuts along the line $f(x)$, producing piece 1 (below $f(x)$) and piece 2 (above $f(x)$). He finds that the ratio of the weights of piece 1 to piece 2 is $R$. Given this, help him find an expression for $\pi$.

## Problem of the Day #302: Optimal PathJanuary 15, 2012

Posted by Albert in : potd , 1 comment so far

Alex is trying to run to Saketh as fast as he can in Coordinatesville. Alex starts off at $(0 \text{m}, 0 \text{m})$ and runs to Saketh at $(10 \text{m} , 10 \text{m})$. Given that Coordinatesville gets increasingly muddy for increasing $x$, such that Alex’s speed $v$ (in meters per second) is given by $v(x) = e^{x^2} \frac{\text{m}}{\text{s}}$, find the minimum amount of time it takes for Alex to reach Saketh.

## Problem of the Day #178: Twins!September 13, 2011

Posted by Seungln in : potd , add a comment

Andrew Tao has finally found his long-lost twin, Tandrew Ao.

## A Tricky ExponentMarch 25, 2011

Posted by Saketh in : calculus , 1 comment so far

Determine the exact value of  $$\int^{\frac{\pi}{2}}_0 \frac{1}{1+(\tan{x})^{\sqrt{2}}} \,dx$$

## An IntegralMarch 25, 2011

Posted by Arjun in : calculus , 3 comments

Find $$\int^{\frac{\pi}{2}}_0 \frac{1}{\sqrt{\tan{x}}} \,dx$$