Using the CAS, the Riemann sum approximation S N , N , N = 1 N 3 ∑ i = 1 N ∑ j = 1 N ∑ k = 1 N f ( i N , j N , k N ) for f ( x , y , z ) = sin ( x y z ) for N = 10 , 20 , a n d 30 , the value of I= ∫ 0 1 ∫ 0 1 ∫ 0 1 f ( x , y , z ) d V and the estimated value of the error | I − S N , N , N | .

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Answer 1

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Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

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Answer 2

Question

Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

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Answer 3

Question

Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

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Answer 4

Question

Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

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Answer 5

Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

Answer 6

Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

Answer 7

Chapter 16.3, Problem 44E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N, N, N} = \frac{1}{N^{3}} \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{k = 1}^{N} f (\frac{i}{N}, \frac{j}{N}, \frac{k}{N})$ for $f (x, y, z) = \sin (x y z)$ for $N = 10, 20, a n d 30$ , the value of I= $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} f (x, y, z) d V$ and the estimated value of the error $| I - S_{N, N, N} |$ .

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

Solution Summary: The author calculates the Riemann sum approximation S N, N and the estimated value of the error.

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Solution Summary: The author calculates the Riemann sum approximation S N, N and the estimated value of the error.

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To calculate: Using the CAS, the Riemann sum approximation SN,N,N=1N3∑i=1N∑j=1N∑k=1Nf(iN,jN,kN) for f(x,y,z)=sin(xyz) for N=10, 20, and 30, the value of I= ∫01∫01∫01f(x,y,z)dV and the estimated value of the error |I−SN,N,N|.

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Chapter 16 Solutions