# Math Help - Lower sum for partition

1. ## Lower sum for partition

f:[0,pi]---R be defined by $f(x)=\sqrt sinx$

by considering the lower sum for the partition P={0,pi/6,5pi/6,pi},prove that $\int_0^{\pi}f\ge\sqrt2pi/3$

$I_1=[0,\pi/6]$, $d_1=\pi/6$

$I_2=[\pi/6,\pi*5/6]$, $d_2=\pi*2/3$

$I_2=[\pi*5/6,\pi]$, $d_3=\pi/6$

$L(f,P)=\sum_{i=1}^3m_id_i$ How do i find $m_i$ for each of the above interval.

Thanks

2. f is increasing on $[0,\pi/2]$ and decreasing on $[\pi/2,\pi]$. On the former, pick the leftmost points. On the later, pick the rightmost points. It doesn't matter on the middle intrval, since its symmetric about the maximum.