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13 Nov 2019
Use Right Reimann sums to estimate the following integral: fx)dx C6.11 . 8,12) K5,8) (7,2) A. 45 O B. 28 C. 26 D. 30 Reset Selection
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Irving Heathcote
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3.) Figure I shows a graph of the function fx)x+6 a) Use a right hand Reimann sum to estimate the area under the graph of fx) over the closed interval [o,2] Use 4 divisions for your estimate. The graph of fx) is shown in Fig.I Fig.1 b) Is your answer in pt. a an overestimate or underestimate? c) Use the First Fundamental Theorem of Calculus to determine the area exactly
Use a calculator to find the value of the following definite integral: J ^49-x2dx 0 A. 21.9911 O B. 49 O c. 76.9690 O D. 153.9380 Reset Selection -7
Recall that if fis integrable on [a, b], then the Definite Integral of f from a to b is given by f(x)dx = lim f(xÇJAxk for any partition of [a, b] and any pointsx. To simplify these calculations, we use equally spaced grid points and right Riemann sums. That is, for each value of n, wlet AxkAand = a + kax, for k = 1,2, , n. Then as n â oo and Îâ 0, k=1 In exercises #1-5, use the definition of the Definite Integral and right Riemann sums to evaluate the following definite integrals. Check your solutions using the Fundamental Theorem of Calculus. (1) x3)dx (2) (2x -4)dx (3) x?dx (4) (x3)dx (5) (2x2-1)dx The following Sums will be of help. Forn a positive integer and c a real number: c=cn k 1 k" = n(n+1)(2n + 1) nn 1)2
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