- 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.
approx. 13 hrs
7 topics
25 concepts
Enhance your conceptual understanding of and skill level in Integration to achieve success in your examinations.
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.
This learning program is made up of the following 7 topics, broken down into 25 concepts.
Area under a curve using sub-intervals
Trapezoidal rule
Simpson's rule
Calculating definite integrals using techniques of integration
Fundamental theorem of calculus, relating the primitive function to an integral
Find indefinite integrals using techniques of integration
Reverse chain rule
Finding the area of a compound region
Odd and even functions in integration
Finding the area between a function and the x axis
Finding the area between a function and the y axis
Differentiate exponential functions involving the chain rule
Integrating functions in the form e^(ax+b)
Application of the derivative of the exponential function
Differentiate exponential functions involving the quotient rule
Differentiate exponential functions involving the product rule
Finding the anti-derivative of an exponential function by considering a derivative
Integrating exponential functions with different bases
Differentiate exponential functions with different bases
Finding the volume of solids of revolution using techniques of integration involving the exponential function
Finding the area of regions using techniques of integration involving the exponential function
Differentiate exponential functions with linear arguments
Reverse chain rule
Find the volume of a solid of revolution about the y axis
Find the volume of a solid of revolution about the x axis
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