Recall That the Average of a Function $f ( x )$

question 35

Multiple Choice

Recall that the average of a function $f ( x )$ on an interval $[ a , b ]$ is $\bar { f } = \frac { 1 } { b - a } \int _ { a } ^ { b } f ( x ) \mathrm { d } x$
Find the average of the given function.
$f ( x ) = \sin ( 5 x )$ over $[ 0,5 \pi ]$

• A)Average = \(\frac { 2 } { 25 \pi }\)
• B) Average = \(\frac { 25 \pi } { 2 }\)
• C) Average = \(\frac { \pi } { 5 }\)
• D) Average = \(\frac { 25 \pi } { 4 }\)
• E) Average = \(\frac { 5 } { \pi }\)

---

Definitions:

New-to-the-world Products

Products that represent a completely new market offering that has never been seen before, often introducing a groundbreaking innovation.

Law of First Movers

The advantage gained by the initial significant occupant of a market segment, often allowing for the establishment of strong brand recognition and customer loyalty.

Amazon Echo

A brand of smart speakers developed by Amazon, integrating the voice-controlled intelligent personal assistant service Alexa to perform a variety of functions and services.

Innovation

The introduction of new ideas, products, services, or processes that create value for businesses, consumers, and society as a whole.