Evaluate the Integral $$\int _ { 0 } ^ { 4 } \left[ - \mathbf { i } - \frac { 2 t } { \left( 7 + t ^ { 2 } \right) ^ { 2 } } j + \frac { 15 } { 2 } \sqrt { t k } \right] d t$$

question 26

Multiple Choice

Evaluate the integral.
- $$\int _ { 0 } ^ { 4 } \left[ - \mathbf { i } - \frac { 2 t } { \left( 7 + t ^ { 2 } \right) ^ { 2 } } j + \frac { 15 } { 2 } \sqrt { t k } \right] d t$$

• A) \(+ 4 i + \frac { 16 } { 161 } j + 40 k\)
• B) \(- 4 i - \frac { 16 } { 161 } j - 40 k\)
• C) \(- 4 i - \frac { 16 } { 161 } j + 40 k\)
• D) \(- 4 i + \frac { 4 } { 77 } j + 40 k\)

---

Definitions:

Cranial Nerves

are the twelve pairs of nerves that emerge directly from the brain, not the spinal cord, and control various functions of the body and head.

Glossopharyngeal

A cranial nerve that innervates parts of the tongue and pharynx, playing roles in taste, swallowing, and salivation.

Hypoglossal

Pertaining to the twelfth cranial nerve, which controls the movements of most muscles in the tongue.

Glossopharyngeal Nerve

The ninth cranial nerve which is responsible for sensory and motor functions in the throat, including taste on the posterior third of the tongue.