Chapter 5: Q39P (page 248)

$\int_{y = 2}^{3} \int_{z = 1}^{2} \int_{x = y + z}^{2 y + z} 6 ydxdzdy$

Short Answer

Expert verified

The solution for the given integral is 70.

Step by step solution

Definition of integration

Integration is a way of finding the whole by adding or summing the parts.

Given Integral

The integral $\int_{y = 2}^{3} \int_{z = 1}^{2} \int_{x = y + z}^{2 y + z} 6 ydxdzdy$ .

To find the value for the given integral.

Finding the integral value

Integrate the given value,

$l = \int_{- 2}^{3} 6 ydy \int_{1}^{2} dz \int_{y + z}^{2 y + 2} dx = \int_{- 2}^{3} 6 ydy \int_{1}^{2} dz (2 y + z - y - z)$

Further Integrating

Now,

$l = \int_{- 2}^{3} 6 ydy \int_{1}^{2} y dz = \int_{- 2}^{3} 6 y^{2} d y \times 1 = {2 y^{3}}_{- 2}^{3} = 70$

Therefore, the required solution for the given integral is 70.

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$\int_{y = 2}^{3} \int_{z = 1}^{2} \int_{x = y + z}^{2 y + z} 6 ydxdzdy$

Short Answer

Step by step solution

Definition of integration

Given Integral

Finding the integral value

Further Integrating

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∫y=23∫z=12∫x=y+z2y+z6ydxdzdy

Short Answer

Step by step solution

Definition of integration

Given Integral

Finding the integral value

Further Integrating

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

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Study anywhere. Anytime. Across all devices.

$\int_{y = 2}^{3} \int_{z = 1}^{2} \int_{x = y + z}^{2 y + z} 6 ydxdzdy$