Integrate the Function $$\int \frac { \left( 49 - t ^ { 2 } \right) ^ { 3 / 2 } } { t ^ { 6 } } d t$$

question 25

Multiple Choice

Integrate the function.
- $$\int \frac { \left( 49 - t ^ { 2 } \right) ^ { 3 / 2 } } { t ^ { 6 } } d t$$

• A) \(- \frac { 1 } { 245 } \left( \frac { \sqrt { 49 - t ^ { 2 } } } { t } \right) ^ { 5 } + \sec ^ { - 1 } \left( \frac { t } { 7 } \right) + C\)
• B) \(- \frac { \left( 49 - t ^ { 2 } \right) ^ { 5 / 2 } } { 245 t ^ { 7 } }\)
• C) \(- \frac { 1 } { 5 } \left( \frac { \sqrt { 49 - t ^ { 2 } } } { t } \right) ^ { 5 } + C\)
• D) \(- \frac { 1 } { 245 } \left( \frac { \sqrt { 49 - t ^ { 2 } } } { t } \right) ^ { 5 } + C\)

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Definitions:

Muscles

Tissues in the body that have the ability to contract, thus enabling movement and support of various body functions.

Joints

The locations at which two or more bones connect, facilitating movement and providing support to the skeletal structure.

Kinesthetic

Relating to kinesthesia, which is the sense that detects bodily position, weight, or movement of the muscles, tendons, and joints.

Perception

The cognitive process of interpreting sensory information to represent and understand the environment around us.