Find the Integral Using an Appropriate Trigonometric Substitution $$\int x \sqrt { 9 - x ^ { 2 } } d x$$

question 74

Multiple Choice

Find the integral using an appropriate trigonometric substitution. $$\int x \sqrt { 9 - x ^ { 2 } } d x$$

• A) \(\frac { 1 } { 3 } x ^ { 2 } \left( 9 - x ^ { 2 } \right) ^ { 3 / 2 } + C\)
• B) \(- \frac { 1 } { 3 } \left( 9 - x ^ { 2 } \right) ^ { 3 / 2 } + C\)
• C) \(- \frac { 1 } { 3 } x ^ { 2 } \left( 9 - x ^ { 2 } \right) ^ { 3 / 2 } + C\)
• D) \(\frac { 1 } { 3 } \left( 9 - x ^ { 2 } \right) ^ { 3 / 2 } + C\)

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Definitions:

Atom

The smallest unit of ordinary matter that forms a chemical element, consisting of a nucleus surrounded by electrons.

Co

Co is the chemical symbol for cobalt, a naturally occurring element with atomic number 27, known for its magnetic properties and use in alloys.

Electrons

Negatively charged subatomic particles that orbit the nucleus of an atom and are involved in chemical bonds and electricity.

Atoms

The basic unit of a chemical element, consisting of a nucleus surrounded by electrons, defining the properties of matter.