- Mathematics Advanced
- Year 12
Integration
approx. 6 hrs
7 topics
25 concepts
Extend your understanding of differential calculus through an in depth look at Integration.
approx. 6 hrs
7 topics
25 concepts
Extend your understanding of differential calculus through an in depth look at Integration.
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.
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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