Integration - Incomplete Flashcards
What are the three cases for intergration of rational functions. I.e I = p(x)/q(x)
1: p(x) is the derivative of q(x)
2: p(x) is higher or equal in degree to q(x)
3: p(x) is lower in degree than q(x)
What is the solution to a type 1 rational function intergration. Where p(x) is the derivative of q(x)
What is the solution to a type 2 rational function. I.e where p(x) is higher or equal in degree to q(x)
Divide the fraction out
What is the solution to a type 3 rational function. p(x) is lower in degree than q(x)
Convert to partial fractions
What is a useful identity for integrating sin^2(x)
sin^2(x) = 0.5(1-cos(2x)
What is a useful substitution for
x = sin(θ)
because we know 1-sin^2(θ) = cos^2(θ)
How do you find the mean value across an interval
What is the notation for mean
- Pointy brackets
What is mean sqaure
What is root mean square
What is the equation for the length of a curve
What is the equation for the length of a parametric arc
What is the equation for the length of a polar curve
What is the equation for a volume of revolution about the y axis
What is the equation for the surface area of a revolved body
What is the equation for a surface area of a revolved body
What is the equation for the centre of mass located on the x axis
What is the equation for the centre of mass located on the y axis
What is the equation for the first moment of area
