Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**●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

●vg. Speed A= b−a

s(b) − s(a)=time

distance

○We can ignore the numerator because it is a constant

○vg. Speed [s(x)] (between a and b)A= 1

b−a

●(x) V(x)S′=

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

●The official formula

○vg. value (t)dta = 1

b−a∫

b

a

V

Example #4

●Find the average value of (x) on [0, ]f=x24

○dx

3

1∫

4

1

x2

■1

b−a= 1

4−1 = 3

1

○( ) (between 1 and 4)

3

13

x3

■Take the integral

○9

43− 9

13= 9

3=3

1

■Plug in values

Average Value

Section 6.5

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Subscribers Only

Example #5

●Given and , what is C?(x) x x Cx 5f= 3− 2 2+ + (x) has an average of 2 on [0, ]f1

●x x

1

b−a∫

1

0

x3− 2 2+C+ 5

○Take the integral

●(x x) (between 0 and 1)

1

14

x4−3

2 3 +2

Cx2+ 5

○Plug in values

●) (0)(4

1−3

2+2

C+ 5 −

○Then simplify

● 2 = 12

6C + 55

●4 55 6C2 − =

● C=6

−31

Example #6

●(x) x on [0, ]f= p1

●Average value of 3

2

●What is ?p

●vg dxa = 1

1−0 ∫

1

0

xp

○Compile the integral

●(between 0 and 1)

p+1

xp+1

○Take the integral

●1

p+2 = 3

2

○Plug in values

● 2(p)3 = + 2

○Simplify

● 2p1 =

● p= 2

1

###### You're Reading a Preview

Unlock to view full version

Subscribers Only