Use the Substitution Formula to Evaluate the Integral $$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$$

question 73

Multiple Choice

Use the substitution formula to evaluate the integral.
- $$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$$

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

Analyze the reasons behind latitudinal gradients in species diversity and the challenges in studying them.

Evaluate the impact of habitat fragmentation and deforestation on biodiversity.

Interpret the role of geographical and climate-related factors in species diversity.

Identify the effects of environmental changes on regional climates and ecosystems.

---

Definitions:

Vegetative Propagation

A process of asexual reproduction in plants where new individuals are formed without the production of seeds or spores.

Fragmentation

A method of asexual reproduction in some bacteria, archaea, animals, or plants; a cell or an organism separates into several pieces and each piece develops into a new organism.

Sporogenesis

The process of spore formation, particularly in plants, fungi, and protozoa.

Fission

The division of a single entity into two or more parts and the regeneration of those parts into separate entities resembling the original.