Use Integration by Parts to Establish a Reduction Formula for the Integral

question 174

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \sec ^ { n } x d x , n \neq 1$$

• A) \(\int \sec ^ { n } x d x = \sec ^ { n - 2 } x \tan x + ( n - 2 ) \int \sec ^ { n - 2 } x d x\)
• B) \(\int \sec ^ { n } x d x = \frac { 1 } { n } \sec ^ { n } x \tan x - \frac { n - 1 } { n } \int \sec ^ { n - 1 } x d x\)
• C) \(\int \sec ^ { n } x d x = \sec ^ { n - 2 } x \tan x - ( n - 2 ) \int \sec ^ { n - 2 } x \tan x d x\)
• D) \(\int \sec ^ { n } x d x = \frac { 1 } { n - 1 } \sec ^ { n - 2 } x \tan x + \frac { n - 2 } { n - 1 } \int \sec ^ { n - 2 } x d x\)

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Definitions:

Depolarization

The process by which the resting potential of a cell membrane becomes less negative, leading to the initiation of an action potential.

Heart Rate

The number of heartbeats per unit of time, usually measured in beats per minute (bpm), indicating the heart's workload and overall cardiovascular health.

Plateau Phase

A phase in some action potentials, notably in cardiac muscle cells, characterized by sustained depolarization that prolongs the action potential.

Cardiac Cycle

Complete round of cardiac systole and diastole.