Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**Section 6.5 - Average Value

●Think about the equation for average speed

○The average speed is the average speed you are at in the time that you traverse

a certain distance

●. = () ()

=

○We can ignore the numerator because it is a constant

○. =

[()] ( )

●() = ()

○The average velocity is average of all the y-values

○

●The official formula

○. =

()

Example #4

●Find the average value of () = [0,4]

○

■

=

=

○

(

) ( 1 4)

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■ Take the integral

○

=

=

■ Plug in values

Example #5

●Given ()= 2 + + 5 and () 2 [0,1], what is

C?

●

2++ 5

○Take the integral

●

(

+

+ 5) ( 0 1)

○Plug in values

●(

+

+ 5) (0)

○Then simplify

●2 =

●24 55 = 6

● =

Example #6

●() = [0,1]

●Average value of

●What is ?

● =

○Compile the integral

●

( 0 1)

○Take the integral

●

=

○Plug in values

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