Integration Higher Mathematics www.maths4scotland.co.uk Next.

Slides:

Advertisements

Similar presentations

Higher Unit 2 Outcome 2 What is Integration

Advertisements

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Higher Unit 3 Differentiation The Chain Rule

Click to start Higher Mathematics Indices Next.

Revision Logarithms & Exponentials Higher Mathematics Next.

Unit 5 : Indices and Surds

1 CALCULUS Even more graphing problems

What are the rules of integral exponents?

Differentiation Higher Mathematics Next.

9.1 Multiplying and Dividing Rational Expressions

Algebraic Fractions and Forming Equations Learning Outcomes  Simplify algebraic fractions  Add, subtract, multiply and divide algebraic fractions  Solve.

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

Higher Unit 3 Further Differentiation Trig Functions Further Integration Integrating Trig Functions Differentiation The Chain Rule.

Example 3 Dividing Mixed Numbers ÷ – 3 19 = 17 6 – Multiply by the reciprocal of 17 6 – 6 – = 3 () 6 – 19 Use rule for multiplying fractions.

Notes Over 8.4 Rewriting Logarithmic Equations Rewrite the equation in exponential form.

Higher Higher Unit 1 What is Integration The Process of Integration Area between to curves Application 1.4.

Motion Graphs Review. Interpret The Graph Below:

Order of Operations.

Order of Operations - rules for arithmetic and algebra that describe what sequence to follow to evaluate an expression involving more than one operation.

Calculus Section 2.4 The Chain Rule. Used for finding the derivative of composite functions Think dimensional analysis Ex. Change 17hours to seconds.

24: Indefinite Integration © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules.

 Multiply Multiply  Divide Divide  Exponent of Exponent Exponent of Exponent  Negative Exponents Negative Exponents  Exponents Video Exponents Video.

MULTIPLYING RATIONAL NUMBERS IF THE SIGNS ARE THE SAME, MULTIPLY THEIR ABSOLUTE VALUES AND THE ANSWER IS POSITIVE. (+4)(+5) = (-4)(-5) = (3)(6) = (-10)(-4)

Notes Over 2.8 Rules for Dividing Negative Numbers. ( Same as Multiplying ) If there is an even number of negative numbers, then the answer is Positive.

Introduction We have seen how to Integrate in C1 In C2 we start to use Integration, to work out areas below curves It is increasingly important in this.

Integrated Mathematics

Unit 2: Integers Unit Review. Multiplying Integers The product of two integers with the same sign is a positive. Eg: (+6) x (+4) = +24; (-18) x (-3) =

Introduction Integration is the reverse process of Differentiation Differentiating gives us a formula for the gradient Integrating can get us the formula.

Higher Higher Unit 2 What is Integration The Process of Integration Integration & Area of a Curve Exam Type.

Multiplying AND DIVIDING RATIONAL EXPRESSIONS. Review: Multiplying fractions.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Order of Operations.

Higher Outcome 2 Higher Unit 3 Further Differentiation Trig Functions Harder Type Questions Further Integration.

position time position time tangent!  Derivatives are the slope of a function at a point  Slope of x vs. t  velocity - describes how position changes.

Bell Quiz. Objectives Simplify rational expressions. Find undefined or excluded values for rational expressions.

Function Notation Assignment. 1.Given f(x) = 6x+2, what is f(3)? Write down the following problem and use your calculator in order to answer the question.

Integers and Absolute Value COURSE 3 LESSON 1-3 Graph the points 2, –3, and 1 on a number line. 1-3.

Integration – Overall Objectives  Integration as the inverse of differentiation  Definite and indefinite integrals  Area under the curve.

To simplify a rational expression, divide the numerator and the denominator by a common factor. You are done when you can no longer divide them by a common.

Coordinates You will need your graph worksheet Interpret the Graph Below: The graph shows an object which is not moving (at rest). The distance stays.

Position, Velocity, and Acceleration Connecting these three things to our knowledge of calculus.

Mathsercise-C Expressions 1 Ready? Here we go!. Expressions 1 Simplify the expression…… 1 4p Question 2 Answer + 9q+ 5p– 3q 9p + 6q.

Motion Graphs. Interpret The Graph Below: The graph shows an object which is not moving (at rest). The distance stays the same as time goes by because.

Interpret The Graph. The graph shows an object which is not moving (at rest). The distance stays the same as time goes by because it is not moving.

Slide 5- 1 Quick Review. Slide 5- 2 Quick Review Solutions.

Notes Over 1.2.

Expanding Brackets and Simplifying

Motion Graphs Position-Time (also called Distance-Time or Displacement-Time) d t At rest.

Bell Work 12/1/14 Pick up a Topic Reinforcement page from the front table. Take a seat and this week into your agenda. Begin working quietly on the Topic.

MTH1170 Differential Equations

Algebra 1 Section 2.3 Subtract real numbers

More U-Substitution: The “Double-U” Substitution with ArcTan(u)

More U-Substitution: The “Double-U” Substitution with ArcTan(u)

Collecting Like terms Brackets 2 Brackets

Integration 2a.

1. Distance vs. time graphs

Objective - To multiply integers.

Integration Higher Mathematics Next.

Exponents and Order of Operations

Notes Over 8.3 Simplifying Natural Base Expressions

Interpreting Graphs.

Section 7.2 Rational Exponents

Distance-time graphs.

9.4 Multiplying & Dividing Rational Expressions

Expanding Brackets with Surds and Fractions

Interpret The Graph.

Presentation transcript:

Integration Higher Mathematics Next

Calculus Revision Back Next Quit Integrate Integrate term by term simplify

Calculus Revision Back Next Quit Find

Calculus Revision Back Next Quit Integrate Multiply out brackets Integrate term by term simplify

Calculus Revision Back Next Quit Find

Calculus Revision Back Next Quit Integrate Standard Integral (from Chain Rule)

Calculus Revision Back Next Quit Find p, given

Calculus Revision Back Next Quit Evaluate Straight line form

Calculus Revision Back Next Quit Find Use standard Integral (from chain rule)

Calculus Revision Back Next Quit Find Integrate term by term

Calculus Revision Back Next Quit Integrate Straight line form

Calculus Revision Back Next Quit Integrate Straight line form

Calculus Revision Back Next Quit Integrate Straight line form

Calculus Revision Back Next Quit Integrate Split into separate fractions

Calculus Revision Back Next Quit Find Use standard Integral (from chain rule)

Calculus Revision Back Next Quit Find

Calculus Revision Back Next Quit Find

Calculus Revision Back Next Quit Integrate Straight line form

Calculus Revision Back Next Quit Given the acceleration a is: If it starts at rest, find an expression for the velocity v where Starts at rest, so v = 0, when t = 0

Calculus Revision Back Next Quit A curve for which passes through the point Find y in terms of x. Use the point

Calculus Revision Back Next Quit Integrate Split into separate fractions Multiply out brackets

Calculus Revision Back Next Quit If passes through the point express y in terms of x. Use the point

Calculus Revision Back Next Quit Integrate Straight line form

Calculus Revision Back Next Quit The graph of passes through the point (1, 2). express y in terms of x. If simplify Use the point Evaluate c

Calculus Revision Back Next Quit Integrate Straight line form

Calculus Revision Back Next Quit A curve for which passes through the point (–1, 2). Express y in terms of x. Use the point

Calculus Revision Back Next Quit Evaluate Cannot use standard integral So multiply out

Calculus Revision Back Next Quit Evaluate Straight line form

Calculus Revision Back Next Quit Evaluate Use standard Integral (from chain rule)

Calculus Revision Back Next Quit The curve passes through the point Find f(x ) use the given point

Calculus Revision Back Next Quit Integrate Integrate term by term

Calculus Revision Back Next Quit Integrate Integrate term by term

Calculus Revision Back Next Quit Evaluate

Quit C P D © CPD 2004