• Mathematical Methods
  • Year 12

Integration

approx. 13 hrs

7 topics

25 concepts

Enhance your conceptual understanding of and skill level in Integration to achieve success in your examinations.

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Available in
ACT NT QLD SA TAS VIC WA

Overview

Integration is a topic that is covered in Year 12 Mathematical Methods and is aligned with outcomes from the Australian curriculum. This program gives students the skills to use different methods of Integration to solve problems, including area under a curve and volume of the solid of revolution. Students also learn how to evaluate mathematical solutions to problems and to communicate such solutions in an appropriate form.

Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 25 concepts.

  • Approximation Methods of Integration 3 concepts

    1. Area under a curve using sub-intervals

    2. Trapezoidal rule

    3. Simpson's rule

  • Definite Integral 2 concepts

    1. Calculating definite integrals using techniques of integration

    2. Fundamental theorem of calculus, relating the primitive function to an integral

  • Indefinite Integral 1 concept

    1. Find indefinite integrals using techniques of integration

  • Using the Chain Rule in Reverse 1 concept

    1. Reverse chain rule

  • Definite Integral and Area 4 concepts

    1. Finding the area of a compound region

    2. Odd and even functions in integration

    3. Finding the area between a function and the x axis

    4. Finding the area between a function and the y axis

  • Calculus and the Exponential Function 12 concepts

    1. Differentiate exponential functions involving the chain rule

    2. Integrating functions in the form e^(ax+b)

    3. Application of the derivative of the exponential function

    4. Differentiate exponential functions involving the quotient rule

    5. Differentiate exponential functions involving the product rule

    6. Finding the anti-derivative of an exponential function by considering a derivative

    7. Integrating exponential functions with different bases

    8. Differentiate exponential functions with different bases

    9. Finding the volume of solids of revolution using techniques of integration involving the exponential function

    10. Finding the area of regions using techniques of integration involving the exponential function

    11. Differentiate exponential functions with linear arguments

    12. Reverse chain rule

  • Volumes of Solids of Revolution 2 concepts

    1. Find the volume of a solid of revolution about the y axis

    2. Find the volume of a solid of revolution about the x axis

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Integration

Reporting

  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

Fully flexible

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