Find the Indefinite Integral $$\int \sqrt { 49 - 4 x ^ { 2 } } d x$$

question 121

Multiple Choice

Find the indefinite integral. $$\int \sqrt { 49 - 4 x ^ { 2 } } d x$$

• A) \(\frac { 49 } { 4 } \sin ^ { - 1 } \left( \frac { 2 x } { 7 } \right) + \frac { 2 x \sqrt { 49 - 4 x ^ { 2 } } } { 3 } + C\)
• B) \(\frac { 49 } { 4 } \sin ^ { - 1 } \left( \frac { 2 x } { 7 } \right) - \frac { x \sqrt { 49 - 4 x ^ { 2 } } } { 3 } + C\)
• C)\(\frac { 49 } { 4 } \sin ^ { - 1 } \left( \frac { 2 x } { 7 } \right) + \frac { x \sqrt { 49 - 4 x ^ { 2 } } } { 2 } + C\)
• D)\(- \frac { 49 } { 4 } \cos ^ { - 1 } \left( \frac { 2 x } { 7 } \right) + \frac { x \sqrt { 49 - 4 x ^ { 2 } } } { 2 } + C\)
• E)\(- \frac { 49 } { 4 } \cos ^ { - 1 } \left( \frac { 2 x } { 7 } \right) - \frac { 3 x \sqrt { 49 - 4 x ^ { 2 } } } { 2 } + C\)

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Definitions:

Subduction

The process by which one tectonic plate moves under another plate and sinks into the mantle as the plates converge.

Plate Boundary

The edges where two or more of Earth's tectonic plates meet, characterized by seismic activity, volcanic eruptions, and the formation of geological features.

Oldest Oceanic Crust

The most ancient sections of Earth's oceanic crust, markedly older than most other ocean floor areas, typically found in the deep ocean basins.

Plate Boundary

The edges where two or more of Earth's tectonic plates meet, which are zones of seismic and volcanic activity.