Integration as the limit of a sum Finding the area under a curve Definite integration allows us to find the area under a curve An estimate for the area under the curve is the sum of the rectangula...
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...
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...
Implicit Differentiation What is implicit differentiation? An equation connecting x and y is not always easy to write explicitly in the form y= f(x) or x = f(y) However you can still differentiate ...
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...
Points of Inflection What is a point of inflection? At AS level you encountered points of inflection when discussing stationary points When the sign of the first derivative (ie of the gradient) is ...
Applications of the Second Derivative What applications of the second derivative do I need to know? The second order derivative (or simply second derivative) is encountered at AS level At AS level ...
Differentiating Reciprocal and Inverse Trig Functions How do I differentiate the reciprocal trigonometric functions? The formulae for the derivatives of the reciprocal trigonometric functions are: ...
Quotient Rule What is the quotient rule? The quotient rule is a formula that allows you to differentiate a quotient of two functions (ie one function divided by another) Exam Tip Worked Exam...
