Chapter 5: Q3P (page 247)

In the problems of this section, set up and evaluate the integrals by hand and check your results by computer $\int_{y = 0}^{2} \int_{x = 2 y}^{4} d x d y$

Short Answer

Expert verified

The required solution is 4.

Step by step solution

Defining Integrals

An integral is a mathematical notion that explains displacement, area, volume, and other ideas that come from the combination of infinitesimal data.

Step 2: Integrating the problem

Integrating with respect to the variable .

$\int_{y = 0}^{2} \int_{x = 2 y}^{4} dxdy = \int_{y = 0}^{2} [\int_{x = 2 y}^{4} dx] dy = \int_{y = 0}^{2} dy (4 - 2 y)$

Further Integrating

Integrating with respect to the variable y.

$\int_{y = 0}^{2} dy (4 - 2 y) = 4 \times y_{0}^{2} - y^{2}_{0}^{2} = 8 (2 - 0) - (4 - 0) = 4$

Therefore, the value is 4.

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In the problems of this section, set up and evaluate the integrals by hand and check your results by computer $\int_{y = 0}^{2} \int_{x = 2 y}^{4} d x d y$

Short Answer

Step by step solution

Defining Integrals

Step 2: Integrating the problem

Further Integrating

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In the problems of this section, set up and evaluate the integrals by hand and check your results by computer∫y=02∫x=2y4dxdy

Short Answer

Step by step solution

Defining Integrals

Step 2: Integrating the problem

Further Integrating

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

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Study anywhere. Anytime. Across all devices.

In the problems of this section, set up and evaluate the integrals by hand and check your results by computer $\int_{y = 0}^{2} \int_{x = 2 y}^{4} d x d y$