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 August 2nd, 2016, 09:16 AM #1 Newbie   Joined: Aug 2016 From: uk Posts: 1 Thanks: 0 Integration, confused I am reading a research paper and I could not understand how the author derived the final equation using integration. Equation A: $Y_L=\frac{1}{1-\beta}\left [\displaystyle\int_0^{N_L}x_L(j)^{1-\beta}\,dj\right ]L^{\beta }$ Equation B: $x_L=\left [\frac{p_L}{\chi_L(j)}\right ]^{1/\beta}L$ Equation C: $Y_L=\frac{1}{1-\beta}p_L^{\frac{1-\beta}{\beta}}N_LL$ where, - $N_L$ is the number of varieties of machines - $x_L$ is the range of machines, so $x_L(j)$ is a machine type $(j)$ - $\chi_L(j)$ is the price of machine type $(j)$ The author uses the equation B in equation A and derives the equation C after integration. It appears, the author replaces $x_L(j)$ in equation A with the equation for $x_L$ which is the equation B. Can anyone please help understand how this could be done? August 2nd, 2016, 03:50 PM #2 Global Moderator   Joined: May 2007 Posts: 6,854 Thanks: 744 Statement A is puzzling. Is j the variable of integration? The description has j a discrete variable. Tags confused, integration Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post nathan Probability and Statistics 4 September 26th, 2014 07:56 AM Shamieh Calculus 3 September 7th, 2013 05:27 PM Siedas Algebra 9 March 10th, 2012 02:29 PM namarsha Real Analysis 2 March 2nd, 2009 04:52 PM ccfoose Calculus 0 December 31st, 1969 04:00 PM

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