Contents Lesson 1 .............................................................................................................................. 2 Lesson#2 ............................................................................................................................. 4 Lesson 3 .............................................................................................................................. 7

OPTIONAL- where it fits in ............................................................................................... 7 Lesson #4 ............................................................................................................................ 9 Lesson #5 .......................................................................................................................... 10 Lesson #6 .......................................................................................................................... 12 Lesson 7 ............................................................................................................................ 13

Lesson #8 .......................................................................................................................... 14 Lesson #9- ......................................................................................................................... 15

Lesson #10 ........................................................................................................................ 18 Lessons 11-13 ................................................................................................................... 19

Lesson #13 ........................................................................................................................ 22

Lesson 1 u-sub from old book WS p 297 # 7-15 odd, 31, 33,44-46,

Flipped classroom

http://www.chaoticgolf.com/vodcasts/calc/lesson6_2_part1/lesson6_2_part1.html

U -substitution Use attached examples from the Greg Kelly power point- examples 1-6

show what can’t be done

When u-substitution does not work

Ex 1 dxxx 35 2

Ex 2 dxxx 22sin5

Ex 3 dxx 32

Ex 4 dxxx 322

Ex 5 dxxx 32 sin

Ex 6 22sin x

Lesson#2 and ln and e to the x-use smart notebook slide 12

cw Worksheet- hw p. 342 #25-43 odd

There's a big calculus party, and all the functions are invited. ln(x) is talking

to some trig functions, when he sees his friend ex sulking in a corner.

ln(x): "What's wrong ex?"

ex: "I'm so lonely!"

ln(x): "Well, you should go integrate yourself into the crowd!"

ex looks up and cries, "It won't make a difference!"

F(x) = eu F’(x) = u’eu chain rule

Review with examples

f(x)=e2x-1 f’(x)=2e2x-1

f(x)=2

5

xe

Examples

dxex x32

dxe x 24

1

0

xe

Integration natural log- examples in smart notebook

xx

dx

d 1ln

'

1ln u

uu

dx

d

Examples-

1.

∫𝟐𝒙

𝒙𝟐+𝟐

2. ∫𝒙𝟐

𝟑𝒙𝟑+𝟕

Don’t get tricked into thinking every integral with division is an ln u

Clarify-From page #320 of book

Because the natural log is undefined for negative number, you will often encounter expressions of the form

ln│u│. The following theorem states that you can differentiate function of the form y=ln│u│ as if the absolute

value sign were not present

dx

x

x

)47tan(

)47(sec2

dx

x

xx

3

53 23

Lesson 3 changing the limits on integration with u-sub- SEGUE FROM YESTERDAY PROBLEMS

IN cw P. 343 # 53-59,63 , 71,73,74,75, (see example #9 on page 341

Do a long division problem-notebook page 17

When u sub does not work

dxe x3

can’t do it

dxe xcos can’t do but can do dxxe xcossin

Integrate

1 3 4 3(2 5)x x dx

4 dx

x

x 3)(ln

2 dxx5

5

5

dx

x

xx 23 34

3

dxx

x29

6. 5x dx

OPTIONAL- where it fits in

Inverse functions 5-3

Reflective property of inverse functions. The graph of f contains the point (a,b) if and only if

the graph of f-1 contains the point (b,a)

Inverse functions undo each other- interchange the x and y and solve for y

F(x) = 2x3-1

G(x)= 3

2

1x

Verify that f(x) and g(x) are inverse functions

F(g(x))=g(f(x))

Listen to it-say it aloud and you can hear it

inverse functions have reciprocal slopes f(x) =2x+3 what is the inverse?

f-1(x) = 1/2x-3/2

what is the slope of f(x) - what is the slope of f-1(x)?

2

F(x) = ¼ x3+x-1

What is f-1(x) when x=3

Chart

X f(x) f’(x)

0 2 1

1 3 2

2 5 3

3 10 4

G(x) = f-1(x)

What is g’(3)

F(x) = 2x2 -3x h(x)=f-1(x) what is h’(-1)_

F’(x) = 6x2-3

What f(-1,1)

h(1,-1) plug in1 into f’(x)

F’(1)=3

So h’(-1)=1/3

Alternate lesson #1-(2012)

Return test, test corrections-

HW- watch video- slope fields and differential equations

http://www.chaoticgolf.com/vodcasts/calc/lesson6_1/lesson6_1.html

Lesson #4 CW- multiple choice- review of FRQ

HW- reverse classroom

Lesson #5

differential equations- HW FRQ 2010 p. 361 #1-5, 7,9,

(Both very good- chaotic golf- does slope fields and differential equations)

http://www.khanacademy.org/video/simple-differential-equations?topic=calculus (15 min)

http://www.chaoticgolf.com/vodcasts/calc/lesson6_1/lesson6_1.html

(20 min) watch 5-11 and 17-22 minute marker

Ex 1-solve the differential 𝑑𝑦

𝑑𝑥 = x y2 use y(1) =2 to solve for C

2) 𝑑𝑦

𝑑𝑥= 4 − 𝑦

3) sinx 𝑑𝑦

𝑑𝑥

= cos x

4) Find the particular solution y=f(x) with initial condition f(0)=-1

𝑦′ =5𝑥

𝑦

Lesson #6 Differential equations-packet- p.4 #5,11 p. 5 #1,2 and FRQ 2000,2003

HW- mr leckie- Differential equations; Growth and Decay

http://www.chaoticgolf.com/vodcasts/calc/lesson6_4/lesson6_4.html

(10 minutes)

Lesson 7 Cw/hw- from packet- Free response 1992, 1989, p4 #6,12 p. 6 #1993

∫𝑒6𝑥+1

𝑒𝑥 𝑑𝑥

2. The rate of change of y is proportional to y. When t=0 y=2 and

when t=2 y=4. What is the value of y when t=3

2 Water flows continuously from a large tank at a rate proportional to the amount of water

remaining in the tank,

There was initially 10,000 cubic feet of water in the tank and at time t=4 hour, 8000 cubic feet

of water remained, what is the value of k in the equation

To the nearest cubic foot, how much water remained in the tank at time t=8 hour

Lesson #8 Intro to slope fields-

http://www.chaoticgolf.com/vodcasts/calc/lesson6_1/lesson6_1.html

pg,2,3

Lesson #9- Slope fields-Packet p. 4,5,6

CW-problems below

Answer 2000 AP calculus BC (homework)

Solution 2005 AP #6

Lesson #10 CW/HW - p. 377 #1-6, 11-14, 37, 39-42

1. Find the general solution to the differential equation: y = y

x

cos

sin.

(Express answer in form y = f(x).)

____________________________________________________________

Lessons 11 Go over HW- ,p. 377 #25-28,32,49

1.

Lesson 12 Reviewp. P. 380 #67-69

9. Write the equation of the curve that passes through the point (1,3) and has a slope of y/x2 at

each point (x,y)

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___

__________________________________________________________

Lesson #13 100 pts AP Style

Integration with u-sub

Differential Equation

Directly proportional differential equation

Slope fields