Q. 0 Problem Zero: Read the section a... [FREE SOLUTION]

Chapter 13: Q. 0 (page 1053)

Problem Zero: Read the section and make your own summary of the material.

Short Answer

Expert verified

If $a_{1} < a_{2}, b_{1} < b_{2}, and c_{1} < c_{2}$ be real numbers, let R be the rectangular solid defined by $R = {(x, y, z) 鈭� a_{1} 鈮� x 鈮� a_{2}, b_{1} 鈮� y 鈮� b_{2}, and c_{1} 鈮� z 鈮� c_{2}}$ and $f (x, y, z)$ is a continuous function defined on R then,

Riemann Sum is defined as ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} f (x_{i}^{鈭�}, y_{j}^{鈭�}, z_{k}^{鈭�}) 螖 V$

and triple integral of f over Ris ${鈭�}_{R} f (x, y, z) d V = lim_{螖鈫� 0} {鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} f (x_{i}^{鈭�}, y_{j}^{鈭�}, z_{k}^{鈭�}) 螖 V$

iterated triple integral is

${鈭�}_{鈩�} f (x, y, z) d V = {鈭�}_{a_{1}}^{a_{2}} {鈭�}_{b_{1}}^{b_{2}} {鈭�}_{c_{1}}^{c_{2}} f (x, y, z) d z d y d x = {鈭�}_{a_{1}}^{a_{2}} ({鈭�}_{b_{1}}^{b_{2}} ({鈭�}_{c_{1}}^{c_{2}} f (x, y, z) d z) d y) d x$

Step by step solution

Step 1. Given information

The given topic of the section is Triple Integrals.

Step 2. Summary

Riemann Sum is defined as ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} f (x_{i}^{鈭�}, y_{j}^{鈭�}, z_{k}^{鈭�}) 螖 V$

iterated triple integral is

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91影视

Problem Zero: Read the section and make your own summary of the material.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Summary

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