Let f(x) = x2 and compute the Riemann sum of f over the interval [7,9], using the following number of subintervals (n). In each case, choose the representative points to be the right endpoints of the subintervals. (Round your answers to two decimal places.)(a) Use two subintervals of equal length (n = 2). (b) Use five subintervals of equal length (n = 5). (c) Use ten subintervals of equal length (n = 10).

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Asked Nov 11, 2019
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Let f(x) = x2 and compute the Riemann sum of f over the interval [7,9], using the following number of subintervals (n). In each case, choose the representative points to be the right endpoints of the subintervals. (Round your answers to two decimal places.)

(a) Use two subintervals of equal length (n = 2).
 

(b) Use five subintervals of equal length (n = 5).
 

(c) Use ten subintervals of equal length (n = 10).

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Expert Answer

Step 1

Find the intervals first. 

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7,b = 9,n = 2. We have that a 9 7 Therefore, A = 1. 2 Divide the interval 7,9] into n 2 subintervals of length Ax = 1: a = [7,8],[8,9] = b

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Step 2

Now, we evaluate the function at the left endpoints.

Finally,  sum up the above values and multiply by delta x=1

1(49+64)=113

Answer(a): 113

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f (x0) = f(a) f (7) = 49 = 49 f (r1)=f(8) 64 = 64

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Step 3

b) Find the interv...

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7,b = 9,n = 5 We have that a 9 7 51 2 Therefore, Ar Divide the interval [7,9] into n 5 subintervals of length Ax 39 41 41 43 37 39 37 a 7, 43 - 5 5 5 5

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