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” –...
Integration using Partial Fractions What are Partial Fractions? This is the reverse process to adding (or subtracting) fractions The common polynomial denominator is split into factors Make sure yo...
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...
Integrating with Trigonometric Identities What are trigonometric identities? Some are given in the formulae booklet Be sure to note the difference between the ± and ∓ symbols! How do I know which t...
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 If then y = ln |x| + c ...
Reverse Chain Rule What is the chain rule? The Chain Rule is a way of differentiating two (or more) functions In many simple cases the above formula/substitution is not needed The same can apply fo...
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 ...
