Use a fiNite Sum to Estimate the Average Value of the Function

question 38

Multiple Choice

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.
- $f ( t ) = 8 - \left( \cos \frac { \pi t } { 2 } \right) ^ { 2 }$ on $[ 0,4 ]$ divided into 4 subintervals

• A) \(\frac { 8 - \sqrt { 2 } } { 2 }\)
• B) \(\frac { 15 } { 2 }\)
• C) 8
• D) \(\frac { 3 } { 2 }\)

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Definitions:

Gross Domestic Product

A measure of the economic performance of a country, calculating the total value of all goods and services produced within its borders in a specific period.

Inputs and Outputs

The resources used in the production process (inputs) and the goods or services produced (outputs).

Pieter Bruegel

A Flemish Renaissance painter known for his landscapes, religious subjects, and depictions of peasant life.

Hunters in the Snow

A famous oil painting by Pieter Bruegel the Elder, depicting a winter scene with hunters and their dogs returning from a hunt, part of a series illustrating different times of the year.