Hi,
Can anyone suggest me how to simplify the integral . If i do integration by parts then how can I solve integral of 1/ sigma term.
Thanks in advance.
\(\displaystyle \documentclass{article}
\usepackage{amssymb,amsmath}
\addtolength{\oddsidemargin}{-1.30in}
\begin{document}
\begin{flushleft}
\begin{align}
\text{ So } \int_a^b\frac{p(y/d)}{p(y/s)}\,dy &= \int_a^b\frac{\frac{1}{n_2h}\sum_{i=1}^{n_2}K\left(\frac{y-y_{i}}{h}\right)}{\frac{1}{n_1h}\sum_{i=1}^{n_1}K\left(\frac{y-y_{i}}{h}\right)} \notag\\
&=\frac{n_1}{n_2}\int_a^b\frac{\sum_{i=1}^{n_2}K\left(\frac{y-y_{i}}{h}\right)}{\sum_{i=1}^{n_1}K\left(\frac{y-y_{i}}{h}\right)}
\notag\\
\text{ where K(x) } &= \frac{3}{4}(1-x^2) \text{ for modulus x<=1} \notag\\
\end{align}
\end{flushleft}
\end{document}\)
Can anyone suggest me how to simplify the integral . If i do integration by parts then how can I solve integral of 1/ sigma term.
Thanks in advance.
\(\displaystyle \documentclass{article}
\usepackage{amssymb,amsmath}
\addtolength{\oddsidemargin}{-1.30in}
\begin{document}
\begin{flushleft}
\begin{align}
\text{ So } \int_a^b\frac{p(y/d)}{p(y/s)}\,dy &= \int_a^b\frac{\frac{1}{n_2h}\sum_{i=1}^{n_2}K\left(\frac{y-y_{i}}{h}\right)}{\frac{1}{n_1h}\sum_{i=1}^{n_1}K\left(\frac{y-y_{i}}{h}\right)} \notag\\
&=\frac{n_1}{n_2}\int_a^b\frac{\sum_{i=1}^{n_2}K\left(\frac{y-y_{i}}{h}\right)}{\sum_{i=1}^{n_1}K\left(\frac{y-y_{i}}{h}\right)}
\notag\\
\text{ where K(x) } &= \frac{3}{4}(1-x^2) \text{ for modulus x<=1} \notag\\
\end{align}
\end{flushleft}
\end{document}\)