Find the Indefinite Integral of the Following Function and Check $\int ( 1 + 4 z ) ^ { 3 } d z$

question 28

Multiple Choice

Find the indefinite integral of the following function and check the result by differentiation. $\int ( 1 + 4 z ) ^ { 3 } d z$

• A) \(4 ( 1 + 4 z ) ^ { 4 } + C\)
• B) \(\frac { ( 1 + 4 z ) ^ { 4 } } { 3 } + C\)
• C) \(\frac { ( 1 + 4 z ) ^ { 4 } } { 4 } + C\)
• D) \(\frac { ( 1 + 4 z ) ^ { 4 } } { 16 } + C\)
• E)none of the above

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Definitions:

Troposphere

The lowest layer of the Earth's atmosphere, where most weather phenomena occur.

Stratosphere

The layer of the Earth's atmosphere located above the troposphere and below the mesosphere, characterized by a slight temperature increase with altitude and the presence of the ozone layer.

Unhealthy Air

Air that is contaminated with pollutants at levels which are harmful to human health and the environment.

Urban Areas

Regions characterized by high human population density and vast human-built features in comparison to the areas surrounding them.