Adding and Subtracting Volumes Why might I need to add or subtract volumes of revolution? As with the area between a curve and a line or the area between 2 curves, a required volume may be created...
Volumes of revolution around the x-axis What is a volume of revolution around the x-axis? A volume of revolution is the volume of this solid formed How do I find the volume of revolution around the...
Area between 2 curves What is the area between two curves? Ensure you are familiar with … Area under a curve Area between a line and a curve In general find the definite integral of “upper curve” –...
Area between a curve and a line What is the area between a curve and a straight line? This is the area enclosed by a curve and a line between their intersections The intersections may need to be fo...
Area Under a Curve What does area under a curve mean? The phrase “area under a curve” refers to the area bounded by … ... the x-axis … the graph of y = f(x) … the vertical line x = a … the vertical...
Improper Integrals What are improper integrals? An improper integral is a definite integral where one or both of the limits is either: Positive or minus infinity A point where the function is undef...
Reverse Chain Rule How do you integrate (ax + b)n? The reverse chain rule can be used for integrating functions in the form y = (ax + b)n Make sure you are confident using the chain rule to differe...
Definite Integration What is definite integration? Definite Integration occurs in an alternative version of the Fundamental Theorem of Calculus This version of the Theorem is the one referred to by...
Integrating Powers of x What is integration? Integration is the inverse ('opposite') of differentiation How do I integrate powers of x? For each term … … increase the power (of x) by 1 … divide b...
Fundamental Theorem of Calculus What is the fundamental theorem of calculus? The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation This form of the T...
Connected Rates of Change What are connected rates of change? In situations involving more than two variables you can use the chain rule to connect multiple rates of change into a single equation E...
Modelling with Differentiation inc. Optimisation How can I use differentiation to solve modelling questions? Derivatives can be calculated for any variables – not just y and x In every case the der...
