Use Reduction Formulas to Evaluate the Integral $$\int \sec ^ { 3 } 4 x d x$$

question 116

Multiple Choice

Use reduction formulas to evaluate the integral.
- $$\int \sec ^ { 3 } 4 x d x$$

• A) \(\frac { 1 } { 8 } \sec ^ { 2 } 4 x \tan 4 x + \frac { 1 } { 8 } \ln | \sec 4 x + \tan 4 x | + C\)
• B) \(\frac { 1 } { 8 } \sec 4 x \tan 4 x + \frac { 1 } { 8 } \ln | \sec 4 x + \tan 4 x | + C\)
• C) \(\frac { 1 } { 8 } \sec 4 x \tan 4 x + \frac { 1 } { 8 } \ln | \sec 4 x + \cot 4 x | + C\)
• D) \(\frac { 1 } { 8 } \sec 4 x \tan 4 x - \frac { 1 } { 4 } \ln | \sec 4 x + \tan 4 x | + C\)

---

Definitions:

Poisson Random Variable

Represents the number of events occurring in a fixed interval of time or space, assuming that these events happen with a known constant mean rate and independently of the time since the last event.

Random Variable

A variable whose possible values are numerical outcomes of a random phenomenon, used in probability and statistics to model randomness.

Expected Value

The anticipated value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

Variance

An indicator of the distance between values in a dataset, reflecting how much each value deviates from the average.