Evaluate the Integral by Making a Substitution and Then Using $$\int \frac { \cos \theta } { \sin \theta \sqrt { 49 + \sin ^ { 2 } \theta } } d \theta$$

question 265

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- $$\int \frac { \cos \theta } { \sin \theta \sqrt { 49 + \sin ^ { 2 } \theta } } d \theta$$

• A) \(- \frac { 1 } { 7 } \ln \left| \frac { 7 + \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta } \right| + C\)
• B) \(- \frac { 1 } { 7 } \ln \left| \frac { 7 \cos \theta + \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta } \right| + C\)
• C) \(- \frac { 1 } { 7 } \ln \left| \frac { 7 - \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta } \right| + C\)
• D) \(- \frac { 1 } { 7 } \ln \left| \frac { 7 + \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta \cos \theta } \right| + C\)

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Definitions:

Tears

The liquid produced by lacrimal glands to lubricate the eyes, containing water, electrolytes, proteins, and lipids.

Tarsal Glands

Sebaceous glands located on the eyelids, responsible for secreting oil that contributes to the tear film.

Oily Substance

Any material with a greasy or slippery consistency, often produced by the sebaceous glands of the skin.

Tears

A secretion from the lacrimal glands used to lubricate the eyes, cleanse them from irritants, and provide antibacterial protection.