• Year 12

# Integration

approx. 6 hrs

7 topics

25 concepts

Extend your understanding of differential calculus through an in depth look at Integration.

Available in
NSW

### Overview

Studying Integration will build on student understanding of differential calculus with a focus on power, logarithmic, exponential and circular functions. The application of integration technques will be extended to find the area under a curve and the volume of a solid of revolution. We will help students master a range of differentiated questions including a mix of practical-related problems.

### 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

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime