Evaluate the Integral by Changing the Order of Integration in an Appropriate

question 264

Multiple Choice

Evaluate the integral by changing the order of integration in an appropriate way.
- $\int _ { 0 } ^ { 1000 } \int _ { \sqrt [ 3 ] { z } } ^ { 10 } \int _ { 1 } ^ { 10,001 } \frac { 1 } { x \left( y ^ { 4 } + 1 \right) } d x d y d z$

• A) \(\frac { \ln 10,001 } { 4 }\)
• B) \(\frac { \ln ^ { 2 } 10,001 } { 4 }\)
• C) \(\frac { \ln ^ { 2 } 10,001 } { 2 }\)
• D) \(\frac { \ln 10,001 } { 2 }\)

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Definitions:

War of 1812

A military conflict fought between the United States and Great Britain from 1812 to 1815, largely over issues of trade and maritime rights.

South and West

Regions often referenced in the context of geographical, cultural, or historical discussions within a specific country, notably the United States.

Old Northwest

A historical term referring to the territorial area northwest of the Ohio River, significant for its early settlement and development of the United States.

War of 1812

A military conflict fought between the United States of America and the United Kingdom, Canadian colonies, and their Native American allies from 1812 to 1815, primarily over issues of trade restrictions and territorial expansion.