SM3 Wks 2,7,8

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8/2/2019 SM3 Wks 2,7,8

2/5

Week 7

Term 1

2012

Theoretical Components

1. Study the examples on integrating special

functions:

Revisit all worked examples in Chapter 9

(9A).

Study Worked Examples (WE) 10-12 in

Chapter 9 (9B) on integrating special

functions (exponential, sine and cosine)

Study examples on basic integration

here:

http://www.intmath.com/integration/2-indefinite-integral.php

2. Watch these youtube video: Approximating

area under a curve using rectangles:

http://www.youtube.com/watch?v=vqSPGeYO2

UA&feature=relmfu

Exact Area under the curve using Definite

integral:

http://www.youtube.com/watch?v=ODwkTt0R

MDg&feature=relmfu3. Read through the notes from Chapter 9 (9D)

from MM12 Quest ebook (Maths Quest 12

Mathematical Methods) and make your notes

on various techniques used to find the

approximate area under the curve.

4. Look at the Resources folder about Simpsons

and Trapezoidal Rules for working out the areas

under curves read and make notes on rules

Practical Components

1. Do few questions in Ex 9A in Yr 12 Methods

Ebook (Q2, Q5, Q7, Q10, Q13, Q14).

2. Do few questions in Ex 9B in Yr 12 Methods

Ebook (Q2-4, Q7, Q10).

3. Do the following questions of Ex 9D from Yr 12

Methods Ebook:

Q1 after you have studied Worked

Example (WE) 18;

Q4 after going through WE19;

Q6 after going through WE20.

4. Use Resources Ex11I and Ex11J to do a

selection of problems on the Trapezoidal and

Simpsons Rules

QuizNext week.

By the end of this week, you should be able to:

Integrate various functions (by hand and by using ClassPad)

Understand the use of areas of rectangles to approximate the area under a

given curve between a defined interval including Simpsons and TrapezoidalRules

Understand the use of sigma notation and limits to approximate area under acurve

Relate the above to idea of finding an exact area under a given curve using

definite integral

IN-CLASS ASSESSMENT:

ANY ONE WHO HAS NOT

YET COMPLETED THE TASKS

SHOULD SEE TOBY ASAP

Goals

Learning BriefSM3: Integral Calculusand Special Functions
http://www.intmath.com/integration/2-indefinite-integral.phphttp://www.intmath.com/integration/2-indefinite-integral.phphttp://www.intmath.com/integration/2-indefinite-integral.phphttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.youtube.com/watch?v=vqSPGeYO2UA&feature=relmfuhttp://www.intmath.com/integration/2-indefinite-integral.phphttp://www.intmath.com/integration/2-indefinite-integral.php

8/2/2019 SM3 Wks 2,7,8

3/5

1. Watch this mini-lecture on Integration:

http://www.intmath.com/integration/integration-mini-lecture-by-

substitution.php

2. Make your notes on the examples shown.

3. Provide additional 2 fully worked examples on Integration by

Substitution.

YOUNEEDTOGETYOURINVESTIGATIONS(FORW

EEKS3,4&5)CHECKEDBYANYMATHSTEACHER!

For

um

Each winter, the Snowy Mountains Authority makes regular measurements of the depth of snow

on the ground in a selected area near some of the major ski resorts. A local newspaper has

published the following graphs snow depth of the 2008 and 2010. Skiers and other visitors find

it interesting to compare the graphs for different years to debate which was the best year for

snow was and which was the worst.

Study the graphs shown below.

Decide which you think were the best and the worst of the years shown. Think about how you

might decide which year was the best for snow and which was the worst.
http://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.phphttp://www.intmath.com/integration/integration-mini-lecture-by-substitution.php

8/2/2019 SM3 Wks 2,7,8

4/5

Week 8

Term 1

2012

Theoretical Components

1. Exact Area under the curve using Definite

integral:

http://www.youtube.com/watch?v=ODwkTt0R

MDg&feature=relmfu

AREA UNDER THE CURVE

http://www.rootmath.org/calculus/area-intro

FUNDAMENTAL THEOREM OF CALCULUS

http://www.rootmath.org/calculus/first-

fundamental-theorem-of-calculusPROPERTIES OF INTEGRATION

http://www.rootmath.org/calculus/properties-

of-integrals

2. Study examples on AREA under the curve:

http://www.intmath.com/applications-

integration/2-area-under-curve.php

3. Area between curves:

http://www.intmath.com/applications-

integration/3-area-between-curves.php

4. Notes on Area under the curve:

http://www.teacherschoice.com.au/maths_libr

ary/calculus/area_under_a_curve.htm

(Focus on the notes/explanations and the

examples, dont have to use Maths Helper Plus)

Practical ComponentsRead the examples and the introduction to the

following Exercises and do the following:

1. Do questions in Ex 9E in Yr 12 Methods Ebook (Q1

(a,d,g,j,m,p,s), Q2 (a,d,g,j,m,p), Q3, Q7-Q9).

2. Do questions in Ex 9F in Yr 12 Methods Ebook (Q3

(all-dont have to evaluate, just write an

expression for finding the area for each),

Q5(a,d,g), Q6).

3. Study the worked examples from Chapter 9H (on

Areas between two curves). Make notes, you

should copy the examples and watch thetutorials)

QuizOn cLc.

By the end of this week, you should be able to:

Integrate various functions (by hand and by using ClassPad), BOTH

INDEFINITE AND DEFINITE INTEGRALS

Understand the use of areas of rectangles to approximate the area under agiven curve between a defined interval

Understand the use of sigma notation and limits to approximate area under a

curve

Relate the above to idea of finding an exact area under a given curve (or

between curves) using definite integral

MINI-LECTURES:NOW RUNNING EVERY

WEDNESDAYS DURING

LUNCH TIME IN ROOM 23.

ALL WELCOME.

Goals

Learning BriefSM3: Integral Calculusand Special Functions

F

O

R

U

M

Next week.
http://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.rootmath.org/calculus/area-introhttp://www.rootmath.org/calculus/area-introhttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/properties-of-integralshttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.teacherschoice.com.au/maths_library/calculus/area_under_a_curve.htmhttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/3-area-between-curves.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.intmath.com/applications-integration/2-area-under-curve.phphttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/properties-of-integralshttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/first-fundamental-theorem-of-calculushttp://www.rootmath.org/calculus/area-introhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfuhttp://www.youtube.com/watch?v=ODwkTt0RMDg&feature=relmfu

8/2/2019 SM3 Wks 2,7,8

5/5

Consider the curve 2 1

1. Integrate the function with respect to x

2. Calculate the Definite integral of this function between -1 and 1

ie 2 1

3. Explain what you find any why the result may not be what you expected.(hint try graphing on your classpad and splitting up areas)

Documents

SM3 Wks 2,7,8