Chapter 13: Q. 49 (page 1055)

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 39 with the order dz dy dx.

Short Answer

Expert verified

The given indicated integral with the specified order of integration is,

$\int_{0}^{2} \int_{0}^{3 - \frac{3}{2} x} \int_{0}^{1 - \frac{1}{2} x - \frac{1}{3} y} f (x, y, z) d z d y d x$

Step by step solution

Step 1. Given Information.

We are given,

$\int_{0}^{4} \int_{0}^{2} \int_{0}^{3 z / 4} f (x, y, z) d x d y d z$

Step 2. Rewriting the integral.

We have to write the given integral in order of dz dy dx .

From the given integral the x varies from $x = 0 to x = 2 - \frac{2}{3} y - 2 z$ and

y varies from $y = 0 to y = 3$ and

z varies from $z = 0 to z = 1 - \frac{y}{3}$

Changing x in terms of y and $z = 0 to z = 1 - \frac{1}{2} y - \frac{1}{3} x$ ,

Similarly on X-Axis y and z are zero so $x = 0 to x = 2$ ,

Changing y in terms of x, $z = 0 to z = 1 - \frac{y}{3}$

Changing the order of integration with respect to $dzdydx$ ,

$\int_{0}^{2} \int_{0}^{3 - \frac{3}{2} x} \int_{0}^{1 - \frac{1}{2} x - \frac{1}{3} y} f (x, y, z) d z d y d x$

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In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 39 with the order dz dy dx.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Rewriting the integral.

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In Exercises 45–52, rewrite the indicated integral with the specified order of integration.Exercise 39 with the order dz dy dx.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Rewriting the integral.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Mechanics Maths

Geometry

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 39 with the order dz dy dx.