Question

3. Find the sum of the areas of approximating rectangles for the area under f(x) = 48 - x?, between x = 1 and x = 5 using 4 subintervals and the right endpoints of each subinterval for sample points. 31

Answer 1

find the Riemann sum for 5 (48 – 2²) dx with in=4 rectangles, using right endpoints. The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a subinterval: f(x)dx ~ Ax (f(x1) + f(x2) + f(x3)+... + f(xn-1) + f(mn)) b- a where A2 n We have that a = 1, b = 5, n = 4. 5 - 1 Therefore, Ax= 571 - = 1. Divide the interval (1,5) into n = 4 subintervals of length Ax = 1: a = [1,2] , [2, 3] , [3, 4], [4, 5] = b.

Now, we just evaluate the function at the right endpoints: f (x1) = f (2) = 44 - 44 f (x2) = f(3) = 39 = 39 f (x3) = f(4) = 32 = 32 f (x4) = f(b) = f (5) = 23 = 23 Finally, just sum up the above values and multiply by Ax = 1: 1(44 +39 + 32 + 23) = 138 Answer: 138

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