Calculate the integral `int_0^4(5-x/2)dx` using Riemann Sum and a regular partition with n subintervals.

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lfryerda | High School Teacher | (Level 2) Educator

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Consider the domain of the integral from x=0 to x=4 and divide it into n equal intervals.  Then each interval has width `Delta x = 4/n` and the `i^{th}` interval has beginning x-value `x_i=iDelta x = {4i}/n` .  This means the function `f(x)=5-x/2` can be evaluated to be `f(x_i)=5-{2i}/n` .  

The area of the `i^{th}` rectangle the domain is then `A_i=f(x_i)Delta x = (5-{2i}/n)4/n=20/n-{8i}/n^2` .

The integral now becomes the sum of the rectangles.







The integral evaluates to 16. 

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