Integrate the Function $\int \frac { \left( 4 - t ^ { 2 } \right) ^ { 3 / 2 } } { t ^ { 6 } } d t$

question 252

Multiple Choice

Integrate the function.
- $\int \frac { \left( 4 - t ^ { 2 } \right) ^ { 3 / 2 } } { t ^ { 6 } } d t$

• A)\( - \frac { \left( 4 - t ^ { 2 } \right) ^ { 5 / 2 } } { 20 t ^ { 7 } }\)
• B) \(- \frac { 1 } { 5 } \left( \frac { \sqrt { 4 - t ^ { 2 } } } { t } \right) ^ { 5 } + C\)
• C)\( - \frac { 1 } { 20 } \left( \frac { \sqrt { 4 - t ^ { 2 } } } { t } \right) ^ { 5 } + \sec ^ { - 1 } \left( \frac { t } { 2 } \right) + C\)
• D) \(- \frac { 1 } { 20 } \left( \frac { \sqrt { 4 - t ^ { 2 } } } { t } \right) ^ { 5 } + C\)

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Definitions:

Forward Rate

The future interest rate agreed upon in a forward contract, which is a derivative financial instrument.

Covered Interest Arbitrage

An investment strategy where an investor takes advantage of the interest rate differential between two countries while hedging exchange rate risk.

Nominal Risk-Free Rate

The nominal risk-free rate is the rate of return on an investment with no risk of financial loss, not adjusted for inflation.

Forward Rate

The agreed-upon interest rate for a financial transaction that will be conducted at a future date.