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 The type of fraction dea...
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 ...
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...
