Find the Integral Using an Appropriate Trigonometric Substitution $$\int \frac { x } { \sqrt { 4 - x ^ { 2 } } } d x$$

question 29

Multiple Choice

Find the integral using an appropriate trigonometric substitution. $$\int \frac { x } { \sqrt { 4 - x ^ { 2 } } } d x$$

• A) \(- \sqrt { 2 - x } + C\)
• B) \(\sqrt { 2 - x } + C\)
• C) \(\sqrt { 4 - x ^ { 2 } } + C\)
• D) \(- \sqrt { 4 - x ^ { 2 } } + C\)

---

Definitions:

Oxiranes

Another term for epoxides, which are three-membered cyclic ethers known for their reactivity and usefulness in synthesizing other compounds.

Oxetanes

Four-membered cyclic ethers with the formula C3H6O, known for their role in organic synthesis, particularly in polymer formulations and drug discovery.

Pyrans

A class of heterocyclic organic compounds characterized by a six-membered ring containing one oxygen atom and five carbon atoms.

Dimethyl Ether

A colorless gas used as a propellant, refrigerant, and solvent, composed of two methyl groups bonded to an oxygen atom.