Integration by Parts What is Integration by Parts? For integrating the product of two functions - reverse product rule Crucially the product is made from u and dv/dx (rather than u and v) Alternati...
Harder Substitution What is integration by substitution? Make sure you are familiar with Reverse Chain Rule and Substitution (RCR) In more difficult questions the substitution will be given to you ...
Substitution (Reverse Chain Rule) What is integration by substitution? Make sure you are familiar with Chain Rule and Reverse Chain Rule In more awkward problems it is harder to spot the reverse ch...
f'(x)/f(x) Integrating fractions The technique for integrating fractions depends on the type of fraction For polynomial denominators see Integration using Partial Fractions The type of fraction dea...
Integrating with Trigonometric Identities What are trigonometric identities? You should be familiar with the trigonometric identities Make sure you can find them in the formula booklet You may need...
Integrating Other Functions (Trig, ln & e etc) Isn’t integration just the reverse of differentiation? Yes, but remember “+c”, the constant of integration … … unless finding a definite integral ...
Parametric Differentiation How do I find dy/dx from parametric equations? Ensure you are familiar with Parametric Equations – Basics first This method uses the chain rule and the reciprocal prop...
Parametric Equations - Sketching Graphs How do I sketch a graph from parametric equations? Plotting a graph is covered in Parametric Equations - Basics Still find the key features of a graph … … t...
Parametric Equations - Eliminating the Parameter What does eliminating the parameter mean? In parametric equations, x = f(t) and y = g(t) There is still a connection directly linking x and y This ...
Parametric Equations - Basics What are parametric equations? Graphs are usually described by a Cartesian equation The equation involves x and y only Equations like this can sometimes be rearranged...
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 ...
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 Example &nb...
