Evaluate the Integral $\int _ { - \frac { \pi } { 4 } } ^ { \frac { \pi } { 4 } } \tan x \mathrm {~d} x$

question 31

Multiple Choice

Evaluate the integral. $\int _ { - \frac { \pi } { 4 } } ^ { \frac { \pi } { 4 } } \tan x \mathrm {~d} x$

• A) \(\ln \left| \sec \left( \frac { \pi } { 4 } \right) \right| - \ln \left| \sec \left( - \frac { \pi } { 4 } \right) \right|\)
• B) \(\ln \left| \sin \left( \frac { \pi } { 4 } \right) \right| - \ln \left| \sin \left( \frac { \pi } { 4 } \right) \right|\)
• C) \(\sin \left( - \frac { \pi } { 4 } \right) - \sin \left( \frac { \pi } { 4 } \right)\)
• D) \(\cos \left( \frac { \pi } { 4 } \right) - \cos \left( - \frac { \pi } { 4 } \right)\)
• E) none of these

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Definitions:

Potential Difference

The difference in electric potential energy per unit charge between two points in a circuit.

Voltage-Gated Channels

Protein channels in cell membranes that open or close in response to changes in electrical potential, allowing ions to pass in and out of the cell.

Repolarization

The process by which cells, particularly nerve and muscle cells, restore their membrane potential to a resting state after depolarization.

All-Or-None Response

A principle that states that nerve or muscle fibers respond to stimuli at their threshold with a complete response or not at all.