November 22nd, 2014, 03:58 PM  #1 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4  Riemann Sums (check my work)
Hi, did I solve this correctly?

November 23rd, 2014, 02:34 AM  #2 
Senior Member Joined: Oct 2014 From: EU Posts: 224 Thanks: 26 Math Focus: Calculus 
Hi Omnipotent, I don't understand how and why you have to divide the area by 4 pieces as such. Maybe the 4 region are the given by the intersections between $\displaystyle x = 0$ and $\displaystyle x = 15$. However, if I should have to determine the area of the triangle you chose with Riemann Integration, I would start expressing the function as a piecewise function: $\displaystyle f(x) = \left\{\begin{matrix} \, 2x \, & \text{if} & x < 5\\ \,x + 15 \, & \text{if} & x \geq 5 \end{matrix}\right. $ Once that, I would calculate: $\displaystyle \int_0^{15} f(x)\,\text{d}x = \int_0^5  2x  \,\text{d}x + \int_5^{15}  x+15  \,\text{d}x$ which is: However, if the 4 regions are given by the intersections of the function, I think (which does not mean I am right) that the lower sum is given by the area of the smallest triangle: In this case the area is given by the Riemann Integral: $\displaystyle \int_0^5 x+15\,\text{d}x \int_0^5 2x\,\text{d}x$ Cheers Last edited by szz; November 23rd, 2014 at 03:28 AM. 
November 24th, 2014, 09:21 AM  #3 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4 
Thank you, however I forgot to add that our professor told us not to use calculus for this problem. He does this thing where first you figure it out the hard way and then u see the trends and then understand the concept. 

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