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:

Urea

A nitrogenous compound produced in the liver as a waste product of protein metabolism.

Uric Acid

A waste product formed from the breakdown of purines, which are found in many foods, and is excreted in urine.

Nephridial Organs

Excretory organs found in many invertebrates, functioning similarly to kidneys in removing metabolic wastes from the organism’s body.

Metanephridia

Excretory organs in many invertebrates, such as annelids, that filter body fluid directly from the coelom.