Integrate the Function $$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$$

question 302

Multiple Choice

Integrate the function.
- $$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$$

• A) \(\frac { 1 } { 9 } \sin ^ { - 1 } \frac { 1 } { 9 }\)
• B) \(\cos ^ { - 1 } \frac { 1 } { 9 }\)
• C) \(9 \cos ^ { - 1 } \frac { 1 } { 9 }\)
• D) \(\sin ^ { - 1 } \frac { 1 } { 9 }\)

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Definitions:

Meteoroid Impact

The collision of a meteoroid with the Earth's surface, capable of producing significant geological features and changes.

Crater

A typically bowl-shaped, steep-sided pit or depression, generally formed by a volcanic eruption or meteorite impact.

Volcanic Explosion

A volcanic explosion occurs when magma, gases, and rocks are violently expelled from a volcano, often with significant force and the potential for widespread impact.

Meteoroid Impact

The collision of a meteoroid (a small rocky or metallic body in outer space) with another celestial body, such as an asteroid, planet, or moon, causing a crater or larger-scale impacts.