Short Answer

Describe the three-dimensional region expressed in each iterated integral:
$\int_{- 2}^{4} \int_{2}^{6} \int_{0}^{5} f (x, y, z) d y d x d z$

$ℝ = {(x, y, z) ∣ 2 \leq x \leq 6, 0 \leq y \leq 5, - 2 \leq z \leq 4}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

We have been given a three-dimensional region:

$\int_{- 2}^{4} \int_{2}^{6} \int_{0}^{5} f (x, y, z) d y d x d z$

We have to describe it in the iterated integral.

Step 2. Evaluate.

By the definition of triple integral $\int_{a_{1}}^{a_{1}} \int_{b_{1}}^{b_{2}} \int_{c_{1}}^{c_{2}} f (x, y, z) d z d y d x$ represent the volume of the solid region $ℝ = \{(x, y, z) ∣ a_{1} \leq x \leq a_{2}, b_{1} \leq y \leq b_{2}, c_{1} \leq z \leq c_{2}\}$

The given triple integral represents the volume of the rectangular solid given by $ℝ = {(x, y, z) ∣ 2 \leq x \leq 6, 0 \leq y \leq 5, - 2 \leq z \leq 4}$

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Calculus

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Short Answer

Describe the three-dimensional region expressed in each iterated integral:
$\int_{- 2}^{4} \int_{2}^{6} \int_{0}^{5} f (x, y, z) d y d x d z$

Step by Step Solution

Step 1. Given information.

Step 2. Evaluate.

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Describe the three-dimensional region expressed in each iterated integral:∫−24 ∫26 ∫05 f(x,y,z)dydxdz

Step by Step Solution

Step 1. Given information.

Step 2. Evaluate.

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Describe the three-dimensional region expressed in each iterated integral:
$\int_{- 2}^{4} \int_{2}^{6} \int_{0}^{5} f (x, y, z) d y d x d z$