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 ...
如果目标高分，A-level和IG考试是具有一定压力的。可是如果目标只是PASS，就轻松很多。那么A-level和IG考多少分算过？ 官方说法，英国政府要求GCSE成绩达到4或以上算过，A-level成绩需要达到E。而高分过（high pa...
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...
