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Integrating standard functions
Integrating f(ax + b)
Integration with trigonometric identities
Reverse chain rule
Integration by substitution
Integration by parts
Integration using partial fractions
Finding areas using integration
The trapezium rule
Solving differential equations
Modelling with differential equations
Differentiating sin x and cos x
Differentiating exponentials and logarithmic functions
The chain rule
The product rule
The quotient rule
Differentiating inverse functions
Differentiating trigonometric functions
Parametric differentiation
Implicit differentiation
Second derivatives: Concave and convex functions
Connected rates of change
Mechanics problems can be modelled using parametric equations. For example, the equations for x and y can represent the displacement and the parameter can represent time.
The best way to solve the problem is by drawing a sketch of the curve and labelling the main points. These can be the points of intersection of the curve with the coordinate axes or the ends of the curve, given by the limits for t. Use a table of values to help.
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