Evaluate the Integral $$\int \frac { d x } { x \sqrt { 16 - x ^ { 2 } } }$$

question 33

Multiple Choice

Evaluate the integral.
- $$\int \frac { d x } { x \sqrt { 16 - x ^ { 2 } } }$$

• A) \(- \frac { 1 } { 4 } \ln \left| \frac { x + \sqrt { 16 - x ^ { 2 } } } { x } \right| + C\)
• B) \(- \frac { 1 } { 4 } \ln \left| \frac { 4 + \sqrt { 16 - x ^ { 2 } } } { x } \right| + C\)
• C) \(- \frac { \sqrt { 16 - x ^ { 2 } } } { 16 x } + C\)
• D) \(\sqrt { 16 - x ^ { 2 } } - 4 \ln \left| \frac { 4 + \sqrt { 16 - x ^ { 2 } } } { x } \right|\)

---

Definitions:

Term Structure

The term structure, often related to interest rates, outlines the relationship between interest rates or yields and different maturity dates for debt securities.

Inflation Premium

The portion of a nominal interest rate that represents compensation for expected future inflation.

Interest Rate Risk

The risk that changes in interest rates will adversely affect the value of an investment, particularly relevant for fixed-income securities.

Bond Prices

The amount of money at which a bond is trading, which fluctuates based on interest rates, credit quality, and other factors.