yr2 chap 11 integration

Cards (7)

  • if a problem contains sin^2x, cos^2x or tan^2x, use trig identities to rearrange it into an easier form
  • if you have a product of two expressions which do not relate to each other, use integration by parts
  • if you have a fraction with multiple factors on the bottom, split it into partial fractions first then use the fact that ln x differentiates to 1/x to integrate the result
  • if you get a question in the form limδx0x=abf(x)δx\lim \delta x \rightarrow 0\:\:\:\:\sum^b_{x=a} f(x)\: \:\delta x, this is a lot easier than it looks, it just means integrate f(x) with an upper limit of b and lower limit of a
  • if a problem is either a product of a function and its derivative, or a quotient of a function and its derivative, use the reverse chain rule
  • to use reverse chain rule with a quotient, try setting y to equal ln of the denominator and differentiating y, then adjust the multiple to make it equal to the numerator
  • to use reverse chain rule with a product, try setting y to equal the function without the derivative and differentiate y, then adjust the multiplke to make it equal to the original