Evaluate the Integral $$\int _ { - \pi / 27 } ^ { \pi / 27 } \sec ^ { 3 } 9 x d x$$

question 434

Multiple Choice

Evaluate the integral.
- $$\int _ { - \pi / 27 } ^ { \pi / 27 } \sec ^ { 3 } 9 x d x$$
Give your answer in exact form.

• A) \(\frac { \sqrt { 3 } } { 9 } + \frac { 1 } { 18 } \ln ( 7 + 4 \sqrt { 3 } )\)
• B) \(\frac { 2 \sqrt { 3 } } { 9 } + \frac { 1 } { 18 } \ln ( 2 \sqrt { 3 } )\)
• C) \(\frac { 2 } { 9 } + \frac { 1 } { 18 } \ln 4\)
• D) \(\frac { 2 \sqrt { 3 } } { 9 } + \frac { 1 } { 18 } \ln ( 7 + 4 \sqrt { 3 } )\)

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Definitions:

Mediastinum

The central compartment of the thoracic cavity between the lungs, containing the heart, esophagus, trachea, and other structures.

Diaphragm

A major muscle involved in breathing, separating the thoracic cavity from the abdominal cavity.

Ligamentum Arteriosum

A small ligament that is the remnant of the ductus arteriosus formed within 3 weeks after birth.

Pulmonary Trunk

A major artery that conducts blood from the right ventricle of the heart to the lungs for oxygenation.